@phdthesis{Imhof2023,
  author    = {Imhof, Stefan Michael},
  title     = {The effects of non-Hermiticity and non-linearity on topological phenomena investigated in electric networks},
  doi       = {10.25972/OPUS-32332},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-323329},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {Topological phenomena known from solid state physics have been transferred to a variety of other classical and quantum systems. Due to the equivalence of the Hamiltonian matrix describing tight binding models and the grounded circuit Laplacian describing an electrical circuit we can investigate such phenomena in circuits. By implementing different Hermitian topological models general suggestions on designing those types of circuit are worked out with the aim of minimizing unwanted coupling effects and parasitic admittances in the circuit. Here the existence and the spatial profile of topological states as well as the band structure of the model can be determined. Due to the complex nature of electric admittance the investigations can be directly expanded to systems with broken Hermiticity. The particular advantages of the experimental investigation of non-exclusively topological phenomena by means of electric circuits come to light in the realization of non-Hermitian and non-linear models. Here we find limitation of the Hermitian bulk-boundary correspondence principle, purely real eigenvalues in non-Hermitian PT-symmetrical systems and edge localization of all eigenstates in non-Hermitian and non-reciprocal systems, which in literature is termed the non-Hermitian skin effect. When systems obeying non-linear equations are studied, the grounded circuit Laplacian based on the Fourier-transform cannot be applied anymore. By combination of the connectivity of a topological system together with non-linear van der Pol oscillators self-activated and self-sustained topological edge oscillations can be found. These robust high frequency sinusoidal edge oscillations differ significantly from low frequency relaxation oscillations, which can be found in the bulk of the system.},
  subject      = {Metamaterial},
  language  = {en}
}
@phdthesis{Stuehler2023,
  author    = {St{\"u}hler, Rudolf Raul Albert},
  title     = {Growth and Spectroscopy of the Two-dimensional Topological Insulator Bismuthene on SiC(0001)},
  doi       = {10.25972/OPUS-32008},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-320084},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {A plethora of novel material concepts are currently being investigated in the condensed matter research community. Some of them hold promise to shape our everyday world in a way that silicon-based semiconductor materials and the related development of semiconductor devices have done in the past. In this regard, the last decades have witnessed an explosion of studies concerned with so called ''quantum materials'' with emerging novel functionalities. These could eventually lead to new generations of electronic and/or spintronic devices. One particular material class, the so called topological materials, play a central role. As far as their technological applicability is concerned, however, they are still facing outstanding challenges to date. Predicted for the first time in 2005 and experimentally verified in 2007, two-dimensional topological insulators (2D TIs) (a.k.a. quantum spin Hall insulators) exhibit the outstanding property of hosting spin-polarized metallic states along the boundaries of the insulating 2D bulk material, which are protected from elastic single-particle backscattering and give rise to the quantum spin Hall effect (QSHE). Owing to these peculiar properties the QSHE holds promise for dissipationless charge and/or spin transport. However, also in today's best 2D TIs the observation of the QSHE is still limited to cryogenic temperatures of maximum 100 K. Here, the discovery of bismuthene on SiC(0001) has marked a milestone towards a possible realization of the QSHE at or beyond room-temperature owing to the massively increased electronic bulk energy gap on the order of 1 eV. This thesis is devoted to and motivated by the goal of advancing its synthesis and to build a deeper understanding of its one-particle and two-particle electronic properties that goes beyond prior work. Regarding the aspect of material synthesis, an improved growth procedure for bismuthene is elaborated that increases the domain size of the material considerably (by a factor of ≈ 3.2 - 6.5 compared to prior work). The improved film quality is an important step towards any future device application of bismuthene, but also facilitates all further basic studies of this material. Moreover, the deposition of magnetic transition metals (Mn and Co) on bismuthene is investigated. Thereby, the formation of ordered magnetic Bi-Mn/Co alloys is realized, their structure is resolved with scanning tunneling microscopy (STM), and their pristine electronic properties are resolved with scanning tunneling spectroscopy (STS) and photoemission spectroscopy (PES). It is proposed that these ordered magnetic Bi-Mn/Co-alloys offer the potential to study the interplay between magnetism and topology in bismuthene in the future. In this thesis, a wide variety of spectroscopic techniques are employed that aim to build an understanding of the single-particle, as well as two-particle level of description of bismuthene's electronic structure. The techniques involve STS and angle-resolved PES (ARPES) on the one hand, but also optical spectroscopy and time-resolved ARPES (trARPES), on the other hand. Moreover, these experiments are accompanied by advanced numerical modelling in form of GW and Bethe-Salpeter equation calculations provided by our theoretical colleagues. Notably, by merging many experimental and theoretical techniques, this work sets a benchmark for electronic structure investigations of 2D materials in general. Based on the STS studies, electronic quasi-particle interferences in quasi-1D line defects in bismuthene that are reminiscent of Fabry-P{\´e}rot states are discovered. It is shown that they point to a hybridization of two pairs of helical boundary modes across the line defect, which is accompanied by a (partial) lifting of their topological protection against elastic single-particle backscattering. Optical spectroscopy is used to reveal bismuthene's two-particle elecronic structure. Despite its monolayer thickness, a strong optical (two-particle) response due to enhanced electron-hole Coulomb interactions is observed. The presented combined experimental and theoretical approach (including GW and Bethe-Salpeter equation calculations) allows to conclude that two prominent optical transitions can be associated with excitonic transitions derived from the Rashba-split valence bands of bismuthene. On a broader scope this discovery might promote further experiments to elucidate links of excitonic and topological physics. Finally, the excited conduction band states of bismuthene are mapped in energy and momentum space employing trARPES on bismuthene for the first time. The direct and indirect band gaps are succesfully extracted and the effect of excited charge carrier induced gap-renormalization is observed. In addition, an exceptionally fast excited charge carrier relaxation is identified which is explained by the presence of a quasi-metallic density of states from coupled topological boundary states of domain boundaries.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{CrespoVidal2023,
  author    = {Crespo Vidal, Can Raphael},
  title     = {Spectroscopic investigation of the three-dimensional topological insulators (MnBi\(_2\)Te\(_4\))(Bi\(_2\)Te\(_3\))\(_n\) and HgTe: band structure, orbital symmetries, and influence of the cation \(d\)-states},
  doi       = {10.25972/OPUS-31293},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-312931},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {This thesis examines the electronic properties of two materials that promise the realization and observation of novel exotic quantum phenomena. For this purpose, angle-resolved photoemission forms the experimental basis for the investigation of the electronic properties. Furthermore, the magnetic order is investigated utilizing X-ray dichroism measurements. First, the bulk and surface electronic structure of epitaxially grown HgTe in its three-dimensional topological insulator phase is investigated. In this study, synchrotron radiation is used to address the three-dimensional band structure and orbital composition of the bulk states by employing photon-energy-dependent and polarization-dependent measurements, respectively. In addition, the topological surface state is examined on in situ grown samples using a laboratory photon source. The resulting data provide a means to experimentally localize the bulk band inversion in momentum space and to evidence the momentum-dependent change in the orbital character of the inverted bulk states. Furthermore, a rather new series of van der Waals compounds, (MnBi\(_2\)Te\(_4\))(Bi\(_2\)Te\(_3\))\(_n\), is investigated. First, the magnetic properties of the first two members of the series, MnBi\(_2\)Te\(_4\) and MnBi\(_4\)Te\(_7\), are studied via X-ray absorption-based techniques. The topological surface state on the two terminations of MnBi\(_4\)Te\(_7\) is analyzed using circular dichroic, photon-energy-dependent, and spin-resolved photoemission. The topological state on the (MnBi\(_2\)Te\(_4\))-layer termination shows a free-standing Dirac cone with its Dirac point located in the bulk band gap. In contrast, on the (Bi\(_2\)Te\(_3\))-layer termination the surface state hybridizes with the bulk valences states, forming a spectral weight gap, and exhibits a Dirac point that is buried within the bulk continuum. Lastly, the lack of unambiguous evidence in the literature showing a temperature-dependent mass gap opening in these magnetic topological insulators is discussed through MnBi\(_2\)Te\(_4\).},
  subject      = {ARPES},
  language  = {en}
}
@phdthesis{Bauernfeind2023,
  author    = {Bauernfeind, Maximilian Josef Xaver},
  title     = {Epitaxy and Spectroscopy of Two-Dimensional Adatom Systems: the Elemental Topological Insulator Indenene on SiC},
  doi       = {10.25972/OPUS-31166},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-311662},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {Two-dimensional (2D) topological insulators are a new class of materials with properties that are promising for potential future applications in quantum computers. For example, stanene represents a possible candidate for a topological insulator made of Sn atoms arranged in a hexagonal lattice. However, it has a relatively fragile low-energy spectrum and sensitive topology. Therefore, to experimentally realize stanene in the topologically non-trivial phase, a suitable substrate that accommodates stanene without compromising these topological properties must be found. A heterostructure consisting of a SiC substrate with a buffer layer of adsorbed group-III elements constitutes a possible solution for this problem. In this work, 2D adatom systems of Al and In were grown epitaxially on SiC(0001) and then investigated structurally and spectroscopically by scanning tunneling microscopy (STM) and photoelectron spectroscopy. Al films in the high coverage regime \( (\Theta_{ML}\approx2\) ML\( ) \) exhibit unusually large, triangular- and rectangular-shaped surface unit cells. Here, the low-energy electron diffraction (LEED) pattern is brought into accordance with the surface topography derived from STM. Another Al reconstruction, the quasi-one-dimensional (1D) Al phase, exhibits a striped surface corrugation, which could be the result of the strain imprinted by the overlayer-substrate lattice mismatch. It is suggested that Al atoms in different surface areas can occupy hexagonal close-packed and face-centered cubic lattice sites, respectively, which in turn lead to close-packed transition regions forming the stripe-like corrugations. On the basis of the well-known herringbone reconstruction from Au(111), a first structural model is proposed, which fits well to the structural data from STM. Ultimately, however, thermal treatments of the sample could not generate lower coverage phases, i.e. in particular, a buffer layer structure. Strong metallic signatures are found for In high coverage films \( (\Theta_{ML}\approx3\) to \(2\) ML\() \) by scanning tunneling spectroscopy (STS) and angle-resolved photoelectron spectroscopy (ARPES), which form a \( (7\times7) \), \( (6\times4\sqrt{3}) \), and \( (4\sqrt{3}\times4\sqrt{3}) \) surface reconstruction. In all these In phases electrons follow the nearly-free electron model. Similar to the Al films, thermal treatments could not obtain the buffer layer system. Surprisingly, in the course of this investigation a triangular In lattice featuring a \( (1\times1) \) periodicity is observed to host massive Dirac-like bands at \( K/K^{\prime} \) in ARPES. Based on this strong electronic similarity with graphene at the Brillouin zone boundary, this new structure is referred to as \textit{indenene}. An extensive theoretical analysis uncovers the emergence of an electronic honeycomb network based on triangularly arranged In \textit{p} orbitals. Due to strong atomic spin-orbit coupling and a comparably small substrate-induced in-plane inversion symmetry breaking this material system is rendered topologically non-trivial. In indenene, the topology is intimately linked to a bulk observable, i.e., the energy-dependent charge accumulation sequence within the surface unit cell, which is experimentally exploited in STS to confirm the non-trivial topological character. The band gap at \( K/K^{\prime} \), a signature of massive Dirac fermions, is estimated by ARPES to approximately 125 meV. Further investigations by X-ray standing wave, STM, and LEED confirm the structural properties of indenene. Thus, this thesis presents the growth and characterization of the novel quantum spin Hall insulator material indenene.},
  subject      = {Dreiecksgitter},
  language  = {en}
}
@phdthesis{Tcakaev2023,
  author    = {Tcakaev, Abdul-Vakhab},
  title     = {Soft X-ray Spectroscopic Study of Electronic and Magnetic Properties of Magnetic Topological Insulators},
  doi       = {10.25972/OPUS-30378},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-303786},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {After the discovery of three-dimensional topological insulators (TIs), such as tetradymite chalcogenides Bi\$_2\$Se\$_3\$, Bi\$_2\$Te\$_3\$ and Sb\$_2\$Te\$_3\$ - a new class of quantum materials characterized by their unique surface electronic properties - the solid state community got focused on topological states that are driven by strong electronic correlations and magnetism. An important material class is the magnetic TI (MTI) exhibiting the quantum anomalous Hall (QAH) effect, i.e. a dissipationless quantized edge-state transport in the absence of external magnetic field, originating from the interplay between ferromagnetism and a topologically non-trivial band structure. The unprecedented opportunities offered by these new exotic materials open a new avenue for the development of low-dissipation electronics, spintronics, and quantum computation. However, the major concern with QAH effect is its extremely low onset temperature, limiting its practical application. To resolve this problem, a comprehensive understanding of the microscopic origin of the underlying ferromagnetism is necessary. V- and Cr-doped (Bi,Sb)\$_2\$Te\$_3\$ are the two prototypical systems that have been widely studied as realizations of the QAH state. Finding microscopic differences between the strongly correlated V and Cr impurities would help finding a relevant model of ferromagnetic coupling and eventually provide better control of the QAH effect in these systems. Therefore, this thesis first focuses on the V- and Cr-doped (Bi,Sb)\$_2\$Te\$_3\$ systems, to better understand these differences. Exploiting the unique capabilities of x-ray absorption spectroscopy and magnetic circular dichroism (XAS/XMCD), combined with advanced modeling based on multiplet ligand-field theory (MLFT), we provide a detailed microscopic insight into the local electronic and magnetic properties of these systems and determine microscopic parameters crucial for the comparison with theoretical models, which include the \$d\$-shell filling, spin and orbital magnetic moments. We find a strongly covalent ground state, dominated by the superposition of one and two Te-ligand-hole configurations, with a negligible contribution from a purely ionic 3+ configuration. Our findings indicate the importance of the Te \$5p\$ states for the ferromagnetism in (Bi, Sb)\$_2\$Te\$_3\$ and favor magnetic coupling mechanisms involving \$pd\$-exchange. Using state-of-the-art density functional theory (DFT) calculations in combination with XMCD and resonant photoelectron spectroscopy (resPES), we reveal the important role of the \$3d\$ impurity states in mediating magnetic exchange coupling. Our calculations illustrate that the kind and strength of the exchange coupling varies with the impurity \$3d\$-shell occupation. We find a weakening of ferromagnetic properties upon the increase of doping concentration, as well as with the substitution of Bi at the Sb site. Finally, we qualitatively describe the origin of the induced magnetic moments at the Te and Sb sites in the host lattice and discuss their role in mediating a robust ferromagnetism based on a \$pd\$-exchange interaction scenario. Our findings reveal important clues to designing higher \$T_{\text{C}}\$ MTIs. Rare-earth ions typically exhibit larger magnetic moments than transition-metal ions and thus promise the opening of a wider exchange gap in the Dirac surface states of TIs, which is favorable for the realization of the high-temperature QAH effect. Therefore, we have further focused on Eu-doped Bi\$_2\$Te\$_3\$ and scrutinized whether the conditions for formation of a substantial gap in this system are present by combining spectroscopic and bulk characterization methods with theoretical calculations. For all studied Eu doping concentrations, our atomic multiplet analysis of the \$M_{4,5}\$ x-ray absorption and magnetic circular dichroism spectra reveals a Eu\$^{2+}\$ valence, unlike most other rare earth elements, and confirms a large magnetic moment. At temperatures below 10 K, bulk magnetometry indicates the onset of antiferromagnetic ordering. This is in good agreement with DFT results, which predict AFM interactions between the Eu impurities due to the direct overlap of the impurity wave functions. Our results support the notion of antiferromagnetism coexisting with topological surface states in rare-earth doped Bi\$_2\$Te\$_3\$ and corroborate the potential of such doping to result in an antiferromagnetic TI with exotic quantum properties. The doping with impurities introduces disorder detrimental for the QAH effect, which may be avoided in stoichiometric, well-ordered magnetic compounds. In the last part of the thesis we have investigated the recently discovered intrinsic magnetic TI (IMTI) MnBi\$_6\$Te\$_{10}\$, where we have uncovered robust ferromagnetism with \$T_{\text{C}} \approx 12\$ K and connected its origin to the Mn/Bi intermixing. Our measurements reveal a magnetically intact surface with a large moment, and with FM properties similar to the bulk, which makes MnBi\$_6\$Te\$_{10}\$ a promising candidate for the QAH effect at elevated temperatures. Moreover, using an advanced ab initio MLFT approach we have determined the ground-state properties of Mn and revealed a predominant contribution of the \$d^5\$ configuration to the ground state, resulting in a \$d\$-shell electron occupation \$n_d = 5.31\$ and a large magnetic moment, in excellent agreement with our DFT calculations and the bulk magnetometry data. Our results together with first principle calculations based on the DFT-GGA\$+U\$, performed by our collaborators, suggest that carefully engineered intermixing plays a crucial role in achieving a robust long-range FM order and therefore could be the key for achieving enhanced QAH effect properties. We expect our findings to aid better understanding of MTIs, which is essential to help increasing the temperature of the QAH effect, thus facilitating the realization of low-power electronics in the future.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Hajer2022,
  author    = {Hajer, Jan},
  title     = {Mercury Telluride Nanowires for Topological Quantum Transport},
  doi       = {10.25972/OPUS-29322},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-293222},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Novel appraches to the molecular beam epitaxy of core-shell nanowires in the group II telluride material system were explored in this work. Significant advances in growth spurred the development of a flexible and reliable platform for a charge transport characterization of the topological insulator HgTe in a tubular nanowire geometry. The transport results presented provide an important basis for the design of future studies that strive for the experimental realization of topological charge transport in the quantum wire limit.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{Schmitt2022,
  author    = {Schmitt, Fabian Bernhard},
  title     = {Transport properties of the three-dimensional topological insulator mercury telluride},
  doi       = {10.25972/OPUS-29173},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-291731},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {The subject of this thesis is the investigation of the transport properties of topological and massive surface states in the three-dimensional topological insulator Hg(Mn)Te. These surface states give rise to a variety of extraordinary transport phenomena, making this material system of great interest for research and technological applications. In this connection, many physical properties of the topological insulator Hg(Mn)Te still require in-depth exploration. The overall aim of this thesis is to analyze the quantum transport of HgTe-based devices ranging from hundreds of micrometers (macroscopic) down to a few micrometers in size (microscopic) in order to extend the overall understanding of surface states and the possibilities of their manipulation. In order to exploit the full potential of our high-quality heterostructures, it was necessary to revise and improve the existing lithographic fabrication process of macroscopic three-dimensional Hg(Mn)Te samples. A novel lithographic standard recipe for the fabrication of the HgTe-based macrostructures was developed. This recipe includes the use of an optimized Hall bar design and wet etching instead of etching with high-energy \(\mathrm{{Ar^{+}}}\)-ions, which can damage the samples. Further, a hafnium oxide insulator is applied replacing the SiO\(_{2}\)/Si\(_{3}\)N\(_{4}\) dielectric in order to reduce thermal load. Moreover, the devices are metallized under an alternating angle to avoid discontinuities of the metal layers over the mesa edges. It was revealed that the application of gate-dielectric and top-gate metals results in n-type doping of the devices. This phenomenon could be attributed to quasi-free electrons tunneling from the trap states, which form at the interface cap layer/insulator, through the cap into the active layer. This finding led to the development of a new procedure to characterize wafer materials. It was found that the optimized lithographic processing steps do not unintentionally react chemically with our heterostructures, thus avoiding a degradation of the quality of the Hg(Mn)Te layer. The implementation of new contact structures Ti/Au, In/Ti/Au, and Al/Ti/Au did not result in any improvement compared to the standard structure AuGe/Au. However, a novel sample recipe could be developed, resulting in an intermixing of the contact metals (AuGe and Au) and fingering of metal into the mesa. The extent of the quality of the ohmic contacts obtained through this process has yet to be fully established. This thesis further deals with the lithographic realization of three-dimensional HgTe-based microstructures measuring only a few micrometer in size. Thus, these structures are in the order of the mean free path and the spin relaxation length of topological surface state electrons. A lithographic process was developed enabling the fabrication of nearly any desired microscopic device structure. In this context, two techniques suitable for etching microscopic samples were realized, namely wet etching and the newly established inductively coupled plasma etching. While wet etching was found to preserve the crystal quality of the active layer best, inductively coupled plasma etching is characterized by high reproducibility and excellent structural fidelity. Hence, the etching technique employed depends on the envisaged type of experiment. Magneto-transport measurements were carried out on the macroscopic HgTe-based devices fabricated by means of improved lithographic processing with respect to the transport properties of topological and massive surface states. It was revealed that due to the low charge carrier density present in the leads to the ohmic contacts, these regions can exhibit an insulating behavior at high magnetic fields and extremely low temperatures. As soon as the filling factor of the lowest Landau levels dropped below a critical value (\(\nu_{\mathrm{{c}}}\approx0.8\)), the conductance of the leads decreased significantly. It was demonstrated that the carrier density in the leads can be increased by the growth of modulation doping layers, a back-gate-electrode, light-emitting diode illumination, and by the application of an overlapping top-gate layout. This overlapping top-gate and a back-gate made it possible to manipulate the carrier density of the surface states on both sides of the Hg(Mn)Te layer independently. With this setup, it was identified that topological and massive surface states contribute to transport simultaneously in 3D Hg(Mn)Te. A model could be developed allowing the charge carrier systems populated in the sample to be determined unambiguously. Based on this model, the process of the re-entrant quantum Hall effect observed for the first time in three-dimensional topological insulators could be explained by an interplay of n-type topological and p-type massive surface states. A well-pronounced \(\nu=-1\rightarrow\nu=-2\rightarrow\nu=-1\) sequence of quantum Hall plateaus was found in manganese-doped HgTe-based samples. It is postulated that this is the condensed-matter realization of the parity anomaly in three-dimensional topological insulators. The actual nature of this phenomenon can be the subject of further research. In addition, the measurements have shown that inter-scattering occurs between counter-propagating quantum Hall edge states. The good quantization of the Hall conductance despite this inter-scattering indicates that only the unpaired edge states determine the transport properties of the system as a whole. The underlying inter-scattering mechanism is the topic of a publication in preparation. Furthermore, three-dimensional HgTe-based microstructures shaped like the capital letter "H" were investigated regarding spin transport phenomena. The non-local voltage signals occurring in the measurements could be attributed to a current-induced spin polarization of the topological surface states due to electrons obeying spin-momentum locking. It was shown that the strength of this non-local signal is directly connected to the magnitude of the spin polarization and can be manipulated by the applied top-gate voltage. It was found that in these microstructures, the massive surface and bulk states, unlike the topological surface states, cannot contribute to this spin-associated phenomenon. On the contrary, it was demonstrated that the population of massive states results in a reduction of the spin polarization, either due to the possible inter-scattering of massive and topological surface states or due to the addition of an unpolarized electron background. The evidence of spin transport controllable by a top-gate-electrode makes the three-dimensional material system mercury telluride a promising candidate for further research in the field of spintronics.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Fijalkowski2022,
  author    = {Fijalkowski, Kajetan Maciej},
  title     = {Electronic Transport in a Magnetic Topological Insulator (V,Bi,Sb)\(_2\)Te\(_3\)},
  doi       = {10.25972/OPUS-28230},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-282303},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {This thesis focuses on investigating magneto-transport properties of a ferromagnetic topological insulator (V,Bi,Sb)2Te3. This material is most famously known for exhibiting the quantum anomalous Hall effect, a novel quantum state of matter that has opened up possibilities for potential applications in quantum metrology as a quantum standard of resistance, as well as for academic investigations into unusual magnetic properties and axion electrodynamics. All of those aspects are investigated in the thesis.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Strunz2022,
  author    = {Strunz, Jonas},
  title     = {Quantum point contacts in HgTe quantum wells},
  doi       = {10.25972/OPUS-27459},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-274594},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Quantenpunktkontakte (englisch: quantum point contacts, QPCs) sind eindimensionale Engstellen in einem ansonsten zweidimensionalen Elektronen- oder Lochsystem. Seit der erstmaligen Realisierung in GaAs-basierten zweidimensionalen Elektronengasen sind QPCs sukzessive zu einem Grundbestandteil mesoskopischer Physik geworden und erfahren in einer Vielzahl von Experimenten Anwendung. Jedoch ist es bis zur Anfertigung der vorliegenden Arbeit nicht gelungen, QPCs in der neuen Materialklasse der zweidimensionalen topologischen Isolatoren zu realisieren. In diesen Materialien tritt der sogenannte Quanten-Spin-Hall-Effekt (QSH-Effekt) auf, welcher sich durch die Ausbildung von leitf{\"a}higen, eindimensionalen sowie gleichermaßen spinpolarisierten Zust{\"a}nden an der Bauteilkante auszeichnet, w{\"a}hrend die restlichen Bereiche der Probe isolierend sind. Ein in einem zweidimensionalen topologischen Isolator realisierter QPC kann demgem{\"a}ß daf{\"u}r benutzt werden, die sich stets an der Bauteilkante befindlichen QSH-Randkan{\"a}le einander r{\"a}umlich anzun{\"a}hern, was beispielsweise die Untersuchung potentieller Wechselwirkungseffekte zwischen ebenjenen Randkan{\"a}len erm{\"o}glicht. Die vorliegende Arbeit beschreibt die erstmalig erfolgreich durchgef{\"u}hrte Implementierung einer QPC-Technologie in einem QSH-System. {\"U}berdies werden die neuartigen Bauteile experimentell charakterisiert sowie analysiert. Nach einer in Kapitel 1 erfolgten Einleitung der Arbeit besch{\"a}ftigt sich das nachfolgende Kapitel 2 zun{\"a}chst mit der besonderen Bandstruktur von HgTe. In diesem Kontext wird die Ausbildung der QSH-Phase f{\"u}r HgTe-Quantentr{\"o}ge mit einer invertierten Bandstruktur erl{\"a}utert, welche f{\"u}r deren Auftreten eine Mindesttrogdicke von d_QW > d_c = 6.3 nm aufweisen m{\"u}ssen. Im Anschluss wird das Konzept eines QPCs allgemein eingef{\"u}hrt sowie das zugeh{\"o}rige Transportverhalten analytisch beschrieben. {\"U}berdies werden die Einschr{\"a}nkungen und Randbedingungen diskutiert, welche bei der Realisierung eines QPCs in einem QSH-System Ber{\"u}cksichtigung finden m{\"u}ssen. Darauf folgt die Pr{\"a}sentation des eigens zur QPC-Herstellung entwickelten Lithographieprozesses, welcher auf einer mehrstufigen Anwendung eines f{\"u}r HgTe-Quantentrogstrukturen geeigneten nasschemischen {\"A}tzverfahrens beruht. Die im Nachgang diskutierten Transportmessungen exemplarischer Proben zeigen die erwartete Leitwertquantisierung in Schritten von ΔG ≈ 2e^2/h im Bereich des Leitungsbandes -- sowohl f{\"u}r eine topologische als auch f{\"u}r eine triviale (d_QW < d_c) QPC-Probe. Mit dem Erreichen der Bandl{\"u}cke saturiert der Leitwert f{\"u}r den topologischen QPC um G_QSH ≈ 2e^2/h, wohingegen ebenjener f{\"u}r den Fall des trivialen Bauteils auf G ≈ 0 abf{\"a}llt. Dar{\"u}ber hinaus belegen durchgef{\"u}hrte Messungen des differentiellen Leitwertes einer invertierten QPC-Probe in Abh{\"a}ngigkeit einer Biasspannung die stabile Koexistenz von topologischen und trivialen Transportmoden. Gegenstand von Kapitel 3 ist die Beschreibung der Ausbildung eines QSH-Interferometers in QPCs mit geringer Weite, welche unter Verwendung von Quantentr{\"o}gen mit einer Trogdicke von d_QW = 7 nm hergestellt werden. Die Diskussion von Bandstrukturrechnungen legt dar, dass die r{\"a}umliche Ausdehnung der Randkan{\"a}le von der jeweiligen Position der Fermi-Energie im Bereich der Bandl{\"u}cke abh{\"a}ngt. Hieraus resultiert eine Transportsituation, in welcher -- unter bestimmten Voraussetzungen -- Reservoir-Elektronen mit randomisiertem Spin an beide QSH-Randkan{\"a}le mit gleicher Wahrscheinlichkeit koppeln, was in der Ausbildung eines QSH-Rings resultiert. Diese Ringbildung wird im Rahmen eines durch Plausibilit{\"a}ts{\"u}berpr{\"u}fung getesteten Modells erkl{\"a}rt und spezifiziert. Danach erfolgt eine theoretische Einf{\"u}hrung von drei relevanten Quantenphasen, deren Akkumulation in der Folge f{\"u}r mehrere geeignete QPC-Proben nachgewiesen wird. Es handelt sich hierbei um die Aharonov-Bohm-Phase, um die dynamische Aharonov-Casher-Phase sowie um eine Spin-Bahn-Berry-Phase mit einem Wert von π. Diese experimentellen Ergebnisse stehen dar{\"u}ber hinaus im Einklang mit analytischen Modellbetrachtungen. Das anschließende Kapitel 4 stellt den letzten Teil der Arbeit dar und besch{\"a}ftigt sich mit der Beobachtung einer anomalen Leitwertsignatur, welche f{\"u}r QPC-Proben basierend auf einer Quantentrogdicke von d_QW = 10.5 nm auftritt. Diese Proben zeigen neben der durch die QSH-Phase bedingten Leitwertquantisierung von G_QSH ≈ 2e^2/h ein weiteres Leitwertplateau mit einem Wert von G ≈ e^2/h = 0.5 x G_QSH. Diese sogenannte 0.5-Anomalie ist nur f{\"u}r ein kleines Intervall von QPC-Weiten beobachtbar und wird mit zunehmender Bauteilweite abgeschw{\"a}cht. Weiterf{\"u}hrende Untersuchungen in Abh{\"a}ngigkeit der Temperatur sowie einer angelegten Biasspannung deuten dar{\"u}ber hinaus darauf hin, dass das Auftreten der 0.5-Anomalie mit einem modifizierten topologischen Zustand einhergeht. {\"U}berdies wird eine zus{\"a}tzliche sowie vervollst{\"a}ndigende Charakterisierung dieses Transportregimes durch die Realisierung eines neuartigen Bauteilkonzeptes m{\"o}glich, welches einen QPC in eine standardisierte Hall-Bar-Geometrie integriert. Das Ergebnis der experimentellen Analyse einer solchen Probe verkn{\"u}pft das Auftreten der 0.5-Anomalie mit der R{\"u}ckstreuung eines QSH-Randkanals. Demgem{\"a}ß wird aus Sicht des Einteilchenbildes geschlussfolgert, dass im Kontext der 0.5-Anomalie lediglich ein Randkanal transmittiert wird. Zudem werden zwei theoretische Modelle basierend auf Elektron-Elektron-Wechselwirkungen diskutiert, welche beide jeweils als urs{\"a}chlicher Mechanismus f{\"u}r das Auftreten der 0.5-Anomalie in Frage kommen. Abschließend ist zu deduzieren, dass die Implementierung einer QPC-Technologie in einem QSH-System eine bedeutende Entwicklung im Bereich der Erforschung von zweidimensionalen topologischen Isolatoren darstellt, welche eine Vielzahl zuk{\"u}nftiger Experimente erm{\"o}glicht. So existieren beispielsweise theoretische Vorhersagen, dass QPCs in einem QSH-System die Detektion von Majorana- sowie Para-Fermionen erm{\"o}glichen. {\"U}berdies ist die nachgewiesene Ausbildung eines QSH-Interferometers in geeigneten QPC-Proben eine Beobachtung von großer Folgewirkung. So erm{\"o}glicht die beobachtete dynamische Aharonov-Casher-Phase im QSH-Regime die kontrollierbare Modulation des topologischen Leitwertes, was die konzeptionelle Grundlage eines topologischen Transistors darstellt. Eine weitere Anwendungsm{\"o}glichkeit wird durch die Widerstandsf{\"a}higkeit geometrischer Phasen gegen{\"u}ber Dephasierung er{\"o}ffnet, wodurch die nachgewiesene Spin-Bahn-Berry-Phase mit einem Wert von π im Kontext potentieller Quantencomputerkonzepte von Interesse ist. Dar{\"u}ber hinaus ist die Transmission von nur einem QSH-Randkanal im Zuge des Auftretens der 0.5-Anomalie {\"a}quivalent zu 100 \% Spinpolarisierung, was einen Faktor essentieller Relevanz f{\"u}r die Realisierung spintronischer Anwendungen darstellt. Demgem{\"a}ß beinhaltet die vorliegende Arbeit den experimentellen Nachweis von drei unterschiedlichen Effekten, von welchen jedem einzelnen eine fundamentale Rolle im Rahmen der Entwicklung neuer Generationen logischer Bauelemente zukommen kann -- erm{\"o}glicht durch die Realisierung von QPCs in topologischen HgTe-Quantentr{\"o}gen.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Riegler2022,
  author    = {Riegler, David},
  title     = {Emergent phenomena in strongly correlated electron systems: Auxiliary particle approach to the many-body problem},
  doi       = {10.25972/OPUS-27473},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-274737},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Emergent phenomena in condensed matter physics like, e.g., magnetism, superconductivity, or non-trivial topology often come along with a surprise and exert great fascination to researchers up to this day. Within this thesis, we are concerned with the analysis of associated types of order that arise due to strong electronic interactions and focus on the high-\(T_c\) cuprates and Kondo systems as two prime candidates. The underlying many-body problem cannot be solved analytically and has given rise to the development of various approximation techniques to tackle the problem. In concrete terms, we apply the auxiliary particle approach to investigate tight-binding Hamiltonians subject to a Hubbard interaction term to account for the screened Coulomb repulsion. Thereby, we adopt the so-called Kotliar-Ruckenstein slave-boson representation that reduces the problem to non-interacting quasiparticles within a mean-field approximation. Part I provides a pedagogical review of the theory and generalizes the established formalism to encompass Gaussian fluctuations around magnetic ground states as a crucial step to obtaining novel results. Part II addresses the two-dimensional one-band Hubbard model, which is known to approximately describe the physics of the high-\(T_c\) cuprates that feature high-temperature superconductivity and various other exotic quantum phases that are not yet fully understood. First, we provide a comprehensive slave-boson analysis of the model, including the discussion of incommensurate magnetic phases, collective modes, and a comparison to other theoretical methods that shows that our results can be massively improved through the newly implemented fluctuation corrections. Afterward, we focus on the underdoped regime and find an intertwining of spin and charge order signaled by divergences of the static charge susceptibility within the antiferromagnetic domain. There is experimental evidence for such inhomogeneous phases in various cuprate materials, which has recently aroused interest because such correlations are believed to impact the formation of Cooper pairs. Our analysis identifies two distinct charge-ordering vectors, one of which can be attributed to a Fermi-surface nesting effect and quantitatively fits experimental data in \(\mathrm{Nd}_{2-\mathrm{x}}\mathrm{Ce}_\mathrm{x}\mathrm{CuO}_4\) (NCCO), an electron-doped cuprate compound. The other resembles the so-called Yamada relation implying the formation of periodic, double-occupied domain walls with a crossover to phase separation for small dopings. Part III investigates Kondo systems by analyzing the periodic Anderson model and its generalizations. First, we consider Kondo metals and detect weakly magnetized ferromagnetic order in qualitative agreement with experimental observations, which hinders the formation of heavy fermions. Nevertheless, we suggest two different parameter regimes that could host a possible Kondo regime in the context of one or two conduction bands. The part is concluded with the study of topological order in Kondo insulators based on a three-dimensional model with centrosymmetric spin-orbit coupling. Thereby, we classify topologically distinct phases through appropriate \(\mathbb{Z}_2\) invariants and consider paramagnetic and antiferromagnetic mean-field ground states. Our model parameters are chosen to specifically describe samarium hexaboride (\(\mbox{SmB}_6\)), which is widely believed to be a topological Kondo insulator, and we identify topologically protected surface states in agreement with experimental evidence in that material. Moreover, our theory predicts the emergence of an antiferromagnetic topological insulator featuring one-dimensional hinge-states as the signature of higher-order topology in the strong coupling regime. While the nature of the true ground state is still under debate, corresponding long-range magnetic order has been observed in pressurized or alloyed \(\mbox{SmB}_6\), and recent experimental findings point towards non-trivial topology under these circumstances. The ability to understand and control topological systems brings forth promising applications in the context of spintronics and quantum computing.},
  subject      = {Elektronenkorrelation},
  language  = {en}
}
@phdthesis{Reis2022,
  author    = {Reis, Felix},
  title     = {Realization and Spectroscopy of the Quantum Spin Hall Insulator Bismuthene on Silicon Carbide},
  doi       = {10.25972/OPUS-25825},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-258250},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Topological matter is one of the most vibrant research fields of contemporary solid state physics since the theoretical prediction of the quantum spin Hall effect in graphene in 2005. Quantum spin Hall insulators possess a vanishing bulk conductivity but symmetry-protected, helical edge states that give rise to dissipationless charge transport. The experimental verification of this exotic state of matter in 2007 lead to a boost of research activity in this field, inspired by possible ground-breaking future applications. However, the use of the quantum spin Hall materials available to date is limited to cryogenic temperatures owing to their comparably small bulk band gaps. In this thesis, we follow a novel approach to realize a quantum spin Hall material with a large energy gap and epitaxially grow bismuthene, i.e., Bi atoms adopting a honeycomb lattice, in a \((\sqrt{3}\times\sqrt{3})\) reconstruction on the semiconductor SiC(0001). In this way, we profit both from the honeycomb symmetry as well as the large spin-orbit coupling of Bi, which, in combination, give rise to a topologically non-trivial band gap on the order of one electronvolt. An in-depth theoretical analysis demonstrates that the covalent bond between the Si and Bi atoms is not only stabilizing the Bi film but is pivotal to attain the quantum spin Hall phase. The preparation of high-quality, unreconstructed SiC(0001) substrates sets the basis for the formation of bismuthene and requires an extensive procedure in ultra-pure dry H\(_2\) gas. Scanning tunneling microscopy measurements unveil the (\(1\times1\)) surface periodicity and smooth terrace planes, which are suitable for the growth of single Bi layers by means of molecular beam epitaxy. The chemical configuration of the resulting Bi film and its oxidation upon exposure to ambient atmosphere are inspected with X-ray photoelectron spectroscopy. Angle-resolved photoelectron spectroscopy reveals the excellent agreement of probed and calculated band structure. In particular, it evidences a characteristic Rashba-splitting of the valence bands at the K point. Scanning tunneling spectroscopy probes signatures of this splitting, as well, and allows to determine the full band gap with a magnitude of \(E_\text{gap}\approx0.8\,\text{eV}\). Constant-current images and local-density-of-state maps confirm the presence of a planar honeycomb lattice, which forms several domains due to different, yet equivalent, nucleation sites of the (\(\sqrt{3}\times\sqrt{3}\))-Bi reconstruction. Differential conductivity measurements demonstrate that bismuthene edge states evolve at atomic steps of the SiC substrate. The probed, metallic local density of states is in agreement with the density of states expected from the edge state's energy dispersion found in density functional theory calculations - besides a pronounced dip at the Fermi level. By means of temperature- and energy-dependent tunneling spectroscopy it is shown that the spectral properties of this suppressed density of states are successfully captured in the framework of the Tomonaga-Luttinger liquid theory and most likely originate from enhanced electronic correlations in the edge channel.},
  subject      = {Zweidimensionales Material},
  language  = {en}
}
@phdthesis{Mueller2022,
  author    = {M{\"u}ller, Valentin Leander},
  title     = {Transport signatures of topological and trivial states in the three-dimensional topological insulator HgTe},
  doi       = {10.25972/OPUS-25952},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-259521},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {The thesis at hand is concerned with improving our understanding of and our control over transport properties of the three-dimensional topological insulator HgTe. Topological insulators are characterized by an insulating bulk and symmetry-protected metallic surface states. These topological surface states hold great promise for research and technology; at the same time, many properties of experimentally accessible topological insulator materials still need to be explored thoroughly. The overall aim of this thesis was to experimentally investigate micrometer-sized HgTe transport devices to observe the ballistic transport regime as well as intercarrier scattering and possibly identify special properties of the topological surface states. Part I of the thesis presents lithographic developments concerned with etching small HgTe devices. The aim was to replace existing processes which relied on dry etching with high-energy \(\text{Ar}^+\) ions and an organic etch mask. This etching method is known to degrade the HgTe crystal quality. In addition, the etch mask turned out to be not durable for long etching processes and difficult to remove completely after etching. First, \(\text{BaF}_2\) was introduced as a new etch mask for dry etching to replace the organic etch mask. With common surface characterization techniques like SEM and XPS it was shown that \(\text{BaF}_2\) etch masks are easy to deposit, highly durable in common dry etching processes for \(\text{Hg}_{1-x}\text{Cd}_x\text{Te}\), and easy to remove in deionized water. Transport results of HgTe devices fabricated with the new etch mask are comparable to results obtained with the old process. At the same time, the new etch mask can withstand longer etching times and does not cause problems due to incomplete removal. Second, a new inductively coupled plasma dry etching process based on \(\text{CH}_4\) and Ar was introduced. This etching process is compatible with \(\text{BaF}_2\) etch masks and yields highly reproducible results. Transport results indicate that the new etching process does not degrade the crystal quality and is suitable to produce high-quality transport devices even in the micrometer range. A comparison with wet-etched samples shows that inductively coupled plasma etching introduces a pronounced edge roughness. This - usually undesirable - property is actually beneficial for some of the experiments in this study and mostly irrelevant for others. Therefore, most samples appearing in this thesis were fabricated with the new process. Part II of the thesis details the advancements made in identifying topological and trivial states which contribute to transport in HgTe three-dimensional topological insulators. To this end, macroscopic Hall bar samples were fabricated from high-quality tensilely strained HgTe layers by means of the improved lithographic processes. All samples were equipped with a top gate electrode, and some also with a modulation doping layer or a back gate electrode to modify the carrier density of the surface states on both sides of the HgTe layer. Due to the high sample quality, Landau levels could be well-resolved in standard transport measurements down to magnetic fields of less than 0.5T. High-resolution measurements of the Landau level dispersion with gate voltage and magnetic field allowed disentangling different transport channels. The main result here is that the upper (electron) branches of the two topological surface states contribute to transport in all experimentally relevant density regimes, while the hole branch is not accessible. Far in n-regime bulk conduction band states give a minor contribution to transport. More importantly, trivial bulk valence band holes come into play close to the charge neutrality point. Further in p-regime, the strong applied gate voltage leads to the formation of two-dimensional, massive hole states at the HgTe surface. The interplay of different states gives rise to rich physics: Top gate-back gate maps revealed that an anticrossing of Landau levels from the two topological surface states occurs at equal filling. A possible explanation for this effect is a weak hybridization of the surface states; however, future studies need to further clarify this point. Furthermore, the superposition of n-type topological and p-type trivial surface states leads to an intriguing Landau level dispersion. The good quantization of the Hall conductance in this situation indicates that the counterpropagating edge states interact with each other. The nature of this interaction will be the topic of further research. Part III of the thesis is focused on HgTe microstructures. These "channel samples" have a typical width of 0.5 to 4µm and a typical length of 5 to 80µm. The quality of these devices benefits particularly from the improved lithographic processes. As a result, the impurity mean free path of the topological surface state electrons is on the order of the device width and transport becomes semiballistic. This was verified by measuring the channel resistance in small magnetic fields in n-regime. The deflection of carriers towards the dissipative channel walls results in a pronounced peak in the magnetoresistance, which scales in a predictable manner with the channel width. To investigate transport effects due to mutual scattering of charge carriers, the differential resistance of channel samples was measured as a function of carrier temperature. Selective heating of the charge carriers - but not the lattice - was achieved by passing a heating current through the channel. Increasing the carrier temperature has two pronounced effects when the Fermi level is situated in proximity to the bulk valence band maximum where the density of states is large. First, when both topological surface state electrons and bulk holes are present, electron-hole scattering leads to a pronounced increase in resistance with increasing carrier temperature. Second, a thermally induced increase of the electron and hole carrier densities reduces the resistance again at higher temperatures. A model considering these two effects was developed, which can well reproduce the experimental results. Current heating experiments in zero-gap HgTe quantum wells and compressively strained HgTe layers are consistent with this model. These observations raise the question as to how electron-hole scattering may affect other transport properties of HgTe-based three-dimensional topological insulators, which is briefly discussed in the outlook.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Mahler2022,
  author    = {Mahler, David},
  title     = {Surface states in the topological material HgTe},
  doi       = {10.25972/OPUS-25398},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-253982},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {The motivation for this work has been contributing a step to the advancement of technology. A next leap in technology would be the realization of a scalable quantum computer. One potential route is via topological quantum computing. A profound understanding of topological materials is thus essential. My work contributes by the investigation of the exemplary topological material HgTe. The focus lies on the understanding of the topological surface states (TSS) and new possibilities to manipulate them appropriately. Traditionally top gate electrodes are used to adjust the carrier density in such semi-conductor materials. We found that the electric field of the top gate can further alter the properties of the HgTe layer. The formation of additional massive Volkov-Pankratov states limits the accessibility of the TSS. The understanding of these states and their interplay with the TSS is necessary to appropriately design devices and to ensure their desired properties. Similarly, I observed the existence and stability of TSSs even without a bandgap in the bulk band structure in the inversion induced Dirac semi-metal phase of compressively strained HgTe. The finding of topological surface states in inversion-induced Dirac semi-metals provides a consistent and simple explanation for the observation reported for \(\text{Cd}_3\text{As}_2\). These observations have only been possible due to the high quality of the MBE grown HgTe layers and the access of different phases of HgTe via strain engineering. As a starting point I performed Magneto-transport measurements on 67 nm thick tensilely strained HgTe layers grown on a CdTe substrate. We observed multiple transport channels in this three-dimensional topological insulator and successfully identified them. Not only do the expected topological surface states exist, but also additional massive surface states have been observed. These additional massive surface states are formed due to the electrical field applied at the top gate, which is routinely used to vary the carrier density in the HgTe layer. The additional massive surface states are called Volkov-Pankratov states after B. A. Volkov and O. A. Pankratov. They predicted the existence of similar massive surface states at the interface of materials with mutually inverted bands. We first found indications for such massive Volkov-Pankratov states in high-frequency compressibility measurements for very high electron densities in a fruitful collaboration with LPA in Paris. Magneto-transport measurements and \(k \cdot p\) calculations revealed that such Volkov-Pankratov states are also responsible for the observed whole transport. We also found indications for similar massive VPS in the electron regime, which coexist with the topological surface states. The topological surface states exist over the full investigated gate range including a regime of pure topological insulator transport. To increase the variability of the topological surface states we introduced a modulation doping layer in the buffer layer. This modulation doping layer also enabled us to separate and identify the top and bottom topological surface states. We used the variability of the bulk band structure of HgTe with strain to engineer the band structure of choice using virtual substrates. The virtual substrates enable us to grow compressively strained HgTe layers that do not possess a bandgap, but instead linear crossing points. These layers are predicted to beDirac semi-metals. Indeed I observed also topological surface states and massive Volkov-Pankratov states in the compressively strained Dirac semi-metal phase. The observation of topological surfaces states also in the Dirac semi-metal phase has two consequences: First, it highlights that no bulk bandgap is necessary to observe topological surface states. Second, the observation of TSS also in the Dirac semi-metal phase emphasizes the importance of the underlying band inversion in this phase. I could not find any clear signatures of the predicted disjoint topological surface states, which are typically called Fermi-arcs. The presence of topological surface states and massive Volkov-Pankratov states offer a simple explanation for the observed quantum Hall effect and other two-dimensional transport phenomena in the class of inversion induced Dirac semi-metals, as \(\text{Cd}_3\text{As}_2\). This emphasizes the importance of the inherent bulk band inversion of different topological materials and provides a consistent and elegant explanation for the observed phenomena in these materials. Additionally, it offers a route to design further experiments, devices, and thus the foundation for the induction of superconductivity and thus topological quantum computing. Another possible path towards quantum computing has been proposed based on the chiral anomaly. The chiral anomaly is an apparent transport anomaly that manifests itself as an additional magnetic field-driven current in three-dimensional topological semimetals with a linear crossing point in their bulk band structure. I observed the chiral anomaly in compressively strained HgTe samples and performed multiple control experiments to identify the observed reduction of the magnetoresistance with the chiral anomaly. First, the dependence of the so-called negative magnetoresistance on the angle and strength of the magnetic field has been shown to fit the expectation for the chiral anomaly. Second, extrinsic effects as scattering could be excluded as a source for the observed negative MR using samples with different mobilities and thus impurity concentrations. Third, the necessity of the linear crossing point has been shown by shifting the electrochemical potential away from the linear crossing points, which diminished the negative magnetoresistance. Fourth, I could not observe a negative magnetoresistance in the three-dimensional topological insulator phase of HgTe. These observations together prove the existence of the chiral anomaly and verify compressively strained HgTe as Dirac semi-metal. Surprisingly, the chiral anomaly is also present in unstrained HgTe samples, which constitute a semi-metal with a quadratic band touching point. This observation reveals the relevance of the Zeeman effect for the chiral anomaly due to the lifting of the spin-degeneracy in these samples. Additionally to the chiral anomaly, the Dirac semi-metal phase of compressively strained HgTe showed other interesting effects. For low magnetic fields, a strong weak-antilocalization has been observed. Such a strong weak-anti-localization correction in a three-dimensional layer is surprising and interesting. Additionally, non-trivial magnetic field strength and direction dependencies have been observed. These include a strong positive magnetoresistance for high magnetic fields, which could indicate a metal-insulator transition. On a more device-oriented note, the semi-metal phase of unstrained HgTe constitutes the lower limit of the by strain engineering adjustable minimal carrier density of the topological surface states and thus of very high mobility. To sum up, topological surface states have been observed in the three-dimensional topological insulator phase and the Dirac semi-metal phase of HgTe. The existence and accessibility of topological surface states are thus independent of the existence of a bandgap in the bulk band structure. The topological surface states can be accompanied by massive Volkov-Pankratov states. These VPS are created by electric fields, which are routinely applied to adjust the carrier density in semiconductor devices. The theoretical predicted chiral anomaly has been observed in the Dirac semi-metal phase of HgTe. In contrast to theoretical predictions, no indications for the Fermi-arc called disjoint surface states have been observed, but instead the topological and massive Volkov-Pankratov surface states have been found. These states are thus expected for all inversion-induced topological materials.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{EliasdosSantos2021,
  author    = {Elias dos Santos, Graciely},
  title     = {Spin-Orbit Torques and Galvanomagnetic Effects Generated by the 3D Topological Insulator HgTe},
  doi       = {10.25972/OPUS-24797},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-247971},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {In meiner Dissertation besch{\"a}ftigte ich mich mit der Frage, ob der 3D topologische Isolator Quecksilbertellurid (3D TI HgTe) ein geeignetes Material f{\"u}r Spintronik-Anwendungen ist. Wir untersuchten Spin-Bahn-Drehmomente, die auf Elektronen beim Tunneln zwischen HgTe und einem angrenzenden Ferromagneten (Permalloy) einwirken. Zun{\"a}chst setzten wir die Methode der Ferromagnetresonanz (SOT-FMR) f{\"u}r diese Untersuchungen ein. Im ersten Teil der Dissertation werden die Leser in die mathematische Beschreibung von Spin- Bahn-Drehmomenten in einem Hybridsystem bestehend aus topologischem Isolator (TI) und Ferromagnet (FM) eingef{\"u}hrt. Des Weiteren werden die Probenherstellung und der Messaufbau f{\"u}r SOT-FMR Messungen besprochen. Unsere SOT-FMR Messungen ergaben, dass bei tiefen Temperaturen (T = 4.2 K) die Normalkomponente (bezogen auf der TI-Oberfl{\"a}che) des Drehmoments groß war. Bei Raumtemperatur konnten im Signal beide Komponenten (parallel und normal zur TI-Oberfl{\"a}che) beobachtet werden. Aus der Symmetrie der Mixing-Spannung (Abbildungen 3.14 und 3.15) schlossen wir, dass 3D TI HgTe ein Spin-Bahn-Drehmoment auf das Elektronensystem des Permalloys {\"u}bertr{\"a}gt. Unsere Untersuchungen zeigten dar{\"u}ber hinaus, dass die Effizienz dieser {\"U}bertragung mit der anderer vorhandener topologischen Isolatoren vergleichbar ist (siehe Abb. 3.17). Abschließend wurden parasit{\"a}re Effekte bei der Absch{\"a}tzung des Spin-Bahn-Drehmoments bzw. andere Interpretationen des Messsignals und seiner Komponenten (z.B., Thermospannungen) ausf{\"u}hrlich diskutiert. Obwohl die hier gezeigten Ergebnisse vermehrt darauf hinweisen, dass der 3D TI HgTe m{\"o}glicherweise effizient f{\"u}r die Anwendung von Spin-Drehmomenten in angrezenden Ferromagneten ist [1], wird dem Leser weiderholt klargemacht, dass parasit{\"a}re Effekte eventuelle das korrekte Schreiben und Lesen der Information in Ferromagneten verunreignigt. Diese sollten auch bei der Interpretation von publizierten Resultaten besonders hohen Spin-Bahn-Drehmoment{\"u}bertragungen in der Literatur ber{\"u}cksichtigt werden [1-3]. Die Nachteile der SOT-FMR-Messmethode f{\"u}hrten zu einerWeiterentwicklung unseres Messkonzepts, bei dem der Ferromagnet durch eine Spin-Valve-Struktur ersetzt wurde. In dieser Messanordnung ist der Stromfluss durch den 3D TI im Gegensatz zu den vorangegangenen Messungen bekannt und die Widerstands{\"a}nderung der Spin-Valve-Struktur kann durch den GMR-Effekt ausgelesen werden. Die Ausrichtung der Magnetisierung des Ferromagneten in den SOT-FMR-Experimenten erforderte es, ein magnetisches Feld von bis zu 300 mT parallel zur TI-Oberfl{\"a}che anzulegen. Motiviert durch diesen Umstand, untersuchten wir den Einfluss eines parallelen Magnetfelds auf den Magnetowiderstand in 3D TI HgTe. Die {\"u}berraschenden Resultate dieser Messungen werden im zweiten Teil der Dissertation beschrieben. Obwohl nichtmagnetisches Quecksilbertellurid untersucht wurde, oszillierte der transversale Magnetowiderstand (Rxy) mit dem Winkel � zwischen der Magnetfeldrichtung (parallel zur Oberfl{\"a}che) und der elektrischen Stromflussrichtung im topologischen Isolator. Dieser Effekt ist eine typische Eigenschaft von ferromagnetischen Materialien und wird planarer Hall-Effekt (PHE) genannt[4, 5]. Magnetowiderstands- (MR-)Oszillationen wurden ebenfalls sowohl im L{\"a}ngswiderstand (Rxx) und im transversalen Widerstand (Rxy) {\"u}ber einen weiten Bereich von magnetischen Feldst{\"a}rken und Ladungstr{\"a}gerdichten des topologischen Isolators beobachtet. Der PHE wurde bereits zuvor in einem anderen TI-Material (Bi2-xSbxTe3) beschrieben [6]. Als physikalischer Mechanismus wurde von den Autoren Elektronenstreuung an magnetisch polarisierten Streuzentren vorgeschlagen. Wir diskutierten sowohl diesen Erkl{\"a}rungsansatz als auch andere Theorievorschl{\"a}ge in der Literatur [7, 8] kritisch. In dieser Doktorarbeit haben wir versucht, der PHE des 3D TI HgTe durch die Asymmetrie in der Bandstruktur dieses Materials zu erkl{\"a}ren. In k.p Bandstrukturrechnungen mit einer 6-Orbital-Basis zeigten wir, dass das Zwischenspiel von Rashba- und Dresselhaus-Spin-Bahn- Wechselwirkung mit dem magnetischen Feld parallel zur TI-Oberfl{\"a}che zu einer Verformung der Fermikontur des Valenzbands von 3D TI-HgTe f{\"u}hrt, welche ihrerseits eine Anisotropie des Leitf{\"a}higkeit bedingt. Die ben{\"o}tigten Magnetfeldst{\"a}rken in diesem Modell waren mit bis zu 40 T jedoch etwa eine Gr{\"o}ßenordnung gr{\"o}ßer als jene in unseren Experimenten. Des Weiteren lieferte eine direkte Berechnung der Zustandsdichten f{\"u}r Bin k I und Bin ? I bisher keine klaren Resultate. Die komplizierte Abh{\"a}ngigkeit der Rashba-Spin-Bahn-Kopplung f{\"u}r p-leitendes HgTe [9] machte es außerdem schwierig, diesen Term in die Bandstrukturrechnung zu inkludieren. Trotz umfangreicher Bem{\"u}hungen, den Ursprung der galvanomagnetischen Effekte im 3D TI HgTe zu verstehen, konnte in dieser Arbeit der Mechanismus des PHE und der MR-Oszillationen nicht eindeutig bestimmt werden. Es gelang jedoch, einige aus der Literatur bekannte Theorien f{\"u}r den PHE und die MR-Oszillationseffekte in topologischen Isolatoren auszuschließen. Die Herausforderung, eine vollst{\"a}ndige theoretische Beschreibung zu entwickeln, die allen experimentellen Aspekten (PHE, Gatespannungsabh{\"a}ngigkeit und MR-Oszillationen) gerecht wird, bleibt weiter bestehen. Abschließend m{\"o}chte die Autorin ihre Hoffnung ausdr{\"u}cken, den Lesern die Komplexit{\"a}t der Fragestellung n{\"a}her gebracht zu haben und sie in die Kunst elektrischer Messungen an topologischen Isolatoren bei angelegtem parallelem Magnetfeld initiiert zu haben.},
  language  = {en}
}
@phdthesis{Winnerlein2020,
  author    = {Winnerlein, Martin},
  title     = {Molecular Beam Epitaxy and Characterization of the Magnetic Topological Insulator (V,Bi,Sb)\(_2\)Te\(_3\)},
  doi       = {10.25972/OPUS-21166},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-211666},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {The subject of this thesis is the fabrication and characterization of magnetic topological insulator layers of (V,Bi,Sb)\(_2\)Te\(_3\) exhibiting the quantum anomalous Hall effect. A major task was the experimental realization of the quantum anomalous Hall effect, which is only observed in layers with very specific structural, electronic and magnetic properties. These properties and their influence on the quantum anomalous Hall effect are analyzed in detail. First, the optimal conditions for the growth of pure Bi\(_2\)Te\(_3\) and Sb\(_2\)Te\(_3\) crystal layers and the resulting structural quality are studied. The crystalline quality of Bi\(_2\)Te\(_3\) improves significantly at higher growth temperatures resulting in a small mosaicity-tilt and reduced twinning defects. The optimal growth temperature is determined as 260\(^{\circ}\)C, low enough to avoid desorption while maintaining a high crystalline quality. The crystalline quality of Sb\(_2\)Te\(_3\) is less dependent on the growth temperature. Temperatures below 230\(^{\circ}\)C are necessary to avoid significant material desorption, though. Especially for the nucleation on Si(111)-H, a low sticking coefficient is observed preventing the coalescence of islands into a homogeneous layer. The influence of the substrate type, miscut and annealing sequence on the growth of Bi\(_2\)Te\(_3\) layers is investigated. The alignment of the layer changes depending on the miscut angle and annealing sequence: Typically, layer planes align parallel to the Si(111) planes. This can enhance the twin suppression due to transfer of the stacking order from the substrate to the layer at step edges, but results in a step bunched layer morphology. For specific substrate preparations, however, the layer planes are observed to align parallel to the surface plane. This alignment avoids displacement at the step edges, which would cause anti-phase domains. This results in narrow Bragg peaks in XRD rocking curve scans due to long-range order in the absence of anti-phase domains. Furthermore, the use of rough Fe:InP(111):B substrates leads to a strong reduction of twinning defects and a significantly reduced mosaicity-twist due to the smaller lattice mismatch. Next, the magnetically doped mixed compound V\(_z\)(Bi\(_{1-x}\)Sb\(_x\))\(_{2-z}\)Te\(_3\) is studied in order to realize the quantum anomalous Hall effect. The addition of V and Bi to Sb\(_2\)Te\(_3\) leads to efficient nucleation on the Si(111)-H surface and a closed, homogeneous layer. Magneto-transport measurements of layers reveal a finite anomalous Hall resistivity significantly below the von Klitzing constant. The observation of the quantum anomalous Hall effect requires the complete suppression of parasitic bulklike conduction due to defect induced carriers. This can be achieved by optimizing the thickness, composition and growth conditions of the layers. The growth temperature is observed to strongly influence the structural quality. Elevated temperatures result in bigger islands, improved crystallographic orientation and reduced twinning. On the other hand, desorption of primarily Sb is observed, affecting the thickness, composition and reproducibility of the layers. At 190\(^{\circ}\)C, desorption is avoided enabling precise control of layer thickness and composition of the quaternary compound while maintaining a high structural quality. It is especially important to optimize the Bi/Sb ratio in the (V,Bi,Sb)\(_2\)Te\(_3\) layers, since by alloying n-type Bi\(_2\)Te\(_3\) and p-type Sb\(_2\)Te\(_3\) charge neutrality is achieved at a specific mixing ratio. This is necessary to shift the Fermi level into the magnetic exchange gap and fully suppress the bulk conduction. The Sb content x furthermore influences the in-plane lattice constant a significantly. This is utilized to accurately determine x even for thin films below 10 nm thickness required for the quantum anomalous Hall effect. Furthermore, x strongly influences the surface morphology: with increasing x the island size decreases and the RMS roughness increases by up to a factor of 4 between x = 0 and x = 1. A series of samples with x varied between 0.56-0.95 is grown, while carefully maintaining a constant thickness of 9 nm and a doping concentration of 2 at.\% V. Magneto-transport measurements reveal the charge neutral point around x = 0.86 at 4.2 K. The maximum of the anomalous Hall resistivity of 0.44 h/e\(^2\) is observed at x = 0.77 close to charge neutrality. Reducing the measurement temperature to 50 mK significantly increases the anomalous Hall resistivity. Several samples in a narrow range of x between 0.76-0.79 show the quantum anomalous Hall effect with the Hall resistivity reaching the von Klitzing constant and a vanishing longitudinal resistivity. Having realized the quantum anomalous Hall effect as the first group in Europe, this breakthrough enabled us to study the electronic and magnetic properties of the samples in close collaborations with other groups. In collaboration with the Physikalisch-Technische Bundesanstalt high-precision measurements were conducted with detailed error analysis yielding a relative de- viation from the von Klitzing constant of (0.17 \(\pm\) 0.25) * 10\(^{-6}\). This is published as the smallest, most precise value at that time, proving the high quality of the provided samples. This result paves the way for the application of magnetic topological insulators as zero-field resistance standards. Non-local magneto-transport measurements were conducted at 15 mK in close collaboration with the transport group in EP3. The results prove that transport happens through chiral edge channels. The detailed analysis of small anomalies in transport measurements reveals instabilities in the magnetic phase even at 15 mK. Their time dependent nature indicates the presence of superparamagnetic contributions in the nominally ferromagnetic phase. Next, the influence of the capping layer and the substrate type on structural properties and the impact on the quantum anomalous Hall effect is investigated. To this end, a layer was grown on a semi-insulating Fe:InP(111)B substrate using the previously optimized growth conditions. The crystalline quality is improved significantly with the mosaicity twist reduced from 5.4\(^{\circ}\) to 1.0\(^{\circ}\). Furthermore, a layer without protective capping layer was grown on Si and studied after providing sufficient time for degradation. The uncapped layer on Si shows perfect quantization, while the layer on InP deviates by about 5\%. This may be caused by the higher crystalline quality, but variations in e.g. Sb content cannot be ruled out as the cause. Overall, the quantum anomalous Hall effect seems robust against changes in substrate and capping layer with only little deviations. Furthermore, the dependence of the quantum anomalous Hall effect on the thickness of the layers is investigated. Between 5-8 nm thickness the material typically transitions from a 2D topological insulator with hybridized top and bottom surface states to a 3D topological insulator. A set of samples with 6 nm, 8 nm, and 9 nm thickness exhibits the quantum anomalous Hall effect, while 5 nm and 15 nm thick layers show significant bulk contributions. The analysis of the longitudinal and Hall conductivity during the reversal of magnetization reveals distinct differences between different thicknesses. The 6 nm thick layer shows scaling consistent with the integer quantum Hall effect, while the 9 nm thick layer shows scaling expected for the topological surface states of a 3D topological insulator. The unique scaling of the 9 nm thick layer is of particular interest as it may be a result of axion electrodynamics in a 3D topological insulator. Subsequently, the influence of V doping on the structural and magnetic properties of the host material is studied systematically. Similarly to Bi alloying, increased V doping seems to flatten the layer surface significantly. With increasing V content, Te bonding partners are observed to increase simultaneously in a 2:3 ratio as expected for V incorporation on group-V sites. The linear contraction of the in-plane and out-of-plane lattice constants with increasing V doping is quantitatively consistent with the incorporation of V\(^{3+}\) ions, possibly mixed with V\(^{4+}\) ions, at the group-V sites. This is consistent with SQUID measurements showing a magnetization of 1.3 \(\mu_B\) per V ion. Finally, magnetically doped topological insulator heterostructures are fabricated and studied in magneto-transport. Trilayer heterostructures with a non-magnetic (Bi,Sb)\(_2\)Te\(_3\) layer sandwiched between two magnetically doped layers are predicted to host the axion insulator state if the two magnetic layers are decoupled and in antiparallel configuration. Magneto-transport measurements of such a trilayer heterostructure with 7 nm undoped (Bi,Sb)\(_2\)Te\(_3\) between 2 nm thick layers doped with 1.5 at.\% V exhibit a zero Hall plateau representing an insulating state. Similar results in the literature were interpreted as axion insulator state, but in the absence of a measurement showing the antiparallel magnetic orientation other explanations for the insulating state cannot be ruled out. Furthermore, heterostructures including a 2 nm thin, highly V doped layer region show an anomalous Hall effect of opposite sign compared to previous samples. A dependency on the thickness and position of the doped layer region is observed, which indicates that scattering at the interfaces causes contributions to the anomalous Hall effect of opposite sign compared to bulk scattering effects. Many interesting phenomena in quantum anomalous Hall insulators as well as axion insulators are still not unambiguously observed. This includes Majorana bound states in quantum anomalous Hall insulator/superconductor hybrid systems and the topological magneto-electric effect in axion insulators. The limited observation temperature of the quantum anomalous Hall effect of below 1 K could be increased in 3D topological insulator/magnetic insulator heterostructures which utilize the magnetic proximity effect. The main achievement of this thesis is the reproducible growth and characterization of (V,Bi,Sb)2Te3 layers exhibiting the quantum anomalous Hall effect. The detailed study of the structural requirements of the quantum anomalous Hall effect and the observation of the unique axionic scaling behavior in 3D magnetic topological insulator layers leads to a better understanding of the nature of this new quantum state. The high-precision measurements of the quantum anomalous Hall effect reporting the smallest deviation from the von Klitzing constant are an important step towards the realization of a zero-field quantum resistance standard.},
  subject      = {Bismutverbindungen},
  language  = {en}
}
@phdthesis{Schnells2019,
  author    = {Schnells, Vera},
  title     = {Fractional Insulators and their Parent Hamiltonians},
  doi       = {10.25972/OPUS-18561},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-185616},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {In the past few years, two-dimensional quantum liquids with fractional excitations have been a topic of high interest due to their possible application in the emerging field of quantum computation and cryptography. This thesis is devoted to a deeper understanding of known and new fractional quantum Hall states and their stabilization in local models. We pursue two different paths, namely chiral spin liquids and fractionally quantized, topological phases. The chiral spin liquid is one of the few examples of spin liquids with fractional statistics. Despite its numerous promising properties, the microscopic models for this state proposed so far are all based on non-local interactions, making the experimental realization challenging. In the first part of this thesis, we present the first local parent Hamiltonians, for which the Abelian and non-Abelian chiral spin liquids are the exact and, modulo a topological degeneracy, unique ground states. We have developed a systematic approach to find an annihilation operator of the chiral spin liquid and construct from it a many-body interaction which establishes locality. For various system sizes and lattice geometries, we numerically find largely gapped eigenspectra and confirm to an accuracy of machine precision the uniqueness of the chiral spin liquid as ground state of the respective system. Our results provide an exact spin model in which fractional quantization can be studied. Topological insulators are one of the most actively studied topics in current condensed matter physics research. With the discovery of the topological insulator, one question emerged: Is there an interaction-driven set of fractionalized phases with time reversal symmetry? One intuitive approach to the theoretical construction of such a fractional topological insulator is to take the direct product of a fractional quantum Hall state and its time reversal conjugate. However, such states are well studied conceptually and do not lead to new physics, as the idea of taking a state and its mirror image together without any entanglement between the states has been well understood in the context of topological insulators. Therefore, the community has been looking for ways to implement some topological interlocking between different spin species. Yet, for all practical purposes so far, time reversal symmetry has appeared to limit the set of possible fractional states to those with no interlocking between the two spin species. In the second part of this thesis, we propose a new universality class of fractionally quantized, topologically ordered insulators, which we name "fractional insulator". Inspired by the fractional quantum Hall effect, spin liquids, and fractional Chern insulators, we develop a wave function approach to a new class of topological order in a two-dimensional crystal of spin-orbit coupled electrons. The idea is simply to allow the topological order to violate time reversal symmetry, while all locally observable quantities remain time reversal invariant. We refer to this situation as "topological time reversal symmetry breaking". Our state is based on the Halperin double layer states and can be viewed as a two-layer system of an ↑-spin and a ↓-spin sphere. The construction starts off with Laughlin states for the ↑-spin and ↓-spin electrons and an interflavor term, which creates correlations between the two layers. With a careful parameter choice, we obtain a state preserving time reversal symmetry locally, and label it the "311-state". For systems of up to six ↑-spin and six ↓-spin electrons, we manage to construct an approximate parent Hamiltonian with a physically realistic, local interaction.},
  subject      = {Spinfl{\"u}ssigkeit},
  language  = {en}
}
@phdthesis{Bendias2018,
  author    = {Bendias, Michel Kalle},
  title     = {Quantum Spin Hall Effect - A new generation of microstructures},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-168214},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2018},
  abstract  = {The presented thesis summarizes the results from four and a half years of intense lithography development on (Cd,Hg)Te/HgTe/(Cd,Hg)Te quantum well structures. The effort was motivated by the unique properties of this topological insulator. Previous work from Molenkamp at al.\ has proven that the transport through such a 2D TI is carried by electrons with opposite spin, counter-propagating in 1D channels along the sample edge. However, up to this thesis, the length of quantized spin Hall channels has never been reported to exceed 4 µm. Therefore, the main focus was put on a reproducible and easy-to-handle fabrication process that reveals the intrinsic material parameters. Every single lithography step in macro as well as microscopic sample fabrication has been re-evaluated. In the Development, the process changes have been presented along SEM pictures, microgaphs and, whenever possible, measurement responses. We have proven the conventional ion milling etch method to damage the remaining mesa and result in drastically lower electron mobilities in samples of microscopic size. The novel KI:I2:HBr wet etch method for macro and microstructure mesa fabrication has been shown to leave the crystalline structure intact and result in unprecedented mobilities, as high as in macroscopic characterization Hall bars. Difficulties, such as an irregular etch start and slower etching of the conductive QW have been overcome by concentration, design and etch flow adaptations. In consideration of the diffusive regime, a frame around the EBL write field electrically decouples the structure mesa from the outside wafer. As the smallest structure, the frame is etched first and guarantees a non-different etching of the conductive layer during the redox reaction. A tube-pump method assures reproducible etch results with mesa heights below 300 nm. The PMMA etch mask is easy to strip and leaves a clean mesa with no redeposition. From the very first attempts, to the final etch process, the reader has been provided with the characteristics and design requirements necessary to enable the fabrication of nearly any mesa shape within an EBL write field of 200 µm. Magneto resistance measurement of feed-back samples have been presented along the development chronology of wet etch method and subsequent lithography steps. With increasing feature quality, more and more physics has been revealed enabling detailed evaluation of smallest disturbances. The following lithography improvements have been implemented. They represent a tool-box for high quality macro and microstructure fabrication on (CdHg)Te/HgTe of almost any kind. The optical positive resist ECI 3027 can be used as wet and as dry etch mask for structure sizes larger than 1 µm. It serves to etch mesa structures larger than the EBL write field. The double layer PMMA is used for ohmic contact fabrication within the EBL write field. Its thickness allows to first dry etch the (Cd,Hg)Te cap layer and then evaporate the AuGe contact, in situ and self-aligned. Because of an undercut, up to 300 nm can be metalized without any sidewalls after the lift-off. An edge channel mismatch within the contact leads can be avoided, if the ohmic contacts are designed to reach close to the sample and beneath the later gate electrode. The MIBK cleaning step prior to the gate application removes PMMA residuals and thereby improves gate and potential homogeneity. The novel low HfO2-ALD process enables insulator growth into optical and EBL lift-off masks of any resolvable shape. Directly metalized after the insulator growth, the self-aligned method results in thin and homogeneous gate electrode reproducibly withholding gate voltages to +-10 V. The optical negative resist ARN 4340 exhibits an undercut when developed. Usable as dry etch mask and lift-off resist, it enables an in-situ application of ohmic contacts first etching close to the QW, then metalizing AuGe. Up to 500 nm thickness, the undercut guarantees an a clean lift-off with no sidewalls. The undertaken efforts have led to micro Hall bar measurements with Hall plateaus and SdH-oszillations in up to now unseen levels of detail. The gap resistance of several micro Hall bars with a clear QSH signal have been presented in Quantum Spin Hall. The first to exhibit longitudinal resistances close to the expected h/2e2 since years, they reveal unprecedented details in features and characteristics. It has been shown that their protection against backscattering through time reversal symmetry is not as rigid as previously claimed. Values below and above 12.9 kΩ been explained, introducing backscattering within the Landauer-B{\"u}ttiker formalism of edge channel transport. Possible reasons have been discussed. Kondo, interaction and Rashba-backscattering arising from density inhomogeneities close to the edge are most plausible to explain features on and deviations from a quantized value. Interaction, tunneling and dephasing mechanisms as well as puddle size, density of states and Rashba Fields are gate voltage dependent. Therefore, features in the QSH signal are fingerprints of the characteristic potential landscape. Stable up to 11 K, two distinct but clear power laws have been found in the higher temperature dependence of the QSH in two samples. However, with ΔR = Tα, α = ¼ in one (QC0285) and α = 2 in the other (Q2745), none of the predicted dependencies could be confirmed. Whereas, the gap resistances of QC0285 remains QSH channel dominated up to 3.9 T and thereby confirmed the calculated lifting of the band inversion in magnetic field. The gate-dependent oscillating features in the QSH signal of Q2745 immediately increase in magnetic field. The distinct field dependencies allowed the assumption of two different dominant backscattering mechanisms. Resulting in undisturbed magneto transport and unprecedented QSH measurements The Novel Micro Hall Bar Process has proven to enable the fabrication of a new generation of microstructures.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{Wiedenmann2018,
  author    = {Wiedenmann, Jonas},
  title     = {Induced topological superconductivity in HgTe based nanostructures},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-162782},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2018},
  abstract  = {This thesis describes the studies of topological superconductivity, which is predicted to emerge when pair correlations are induced into the surface states of 2D and 3D topolog- ical insulators (TIs). In this regard, experiments have been designed to investigate the theoretical ideas first pioneered by Fu and Kane that in such system Majorana bound states occur at vortices or edges of the system [Phys. Rev. Lett. 100, 096407 (2008), Phys. Rev. B 79, 161408 (2009)]. These states are of great interest as they constitute a new quasiparticle which is its own antiparticle and can be used as building blocks for fault tolerant topological quantum computing. After an introduction in chapter 1, chapter 2 of the thesis lays the foundation for the understanding of the field of topology in the context of condensed matter physics with a focus on topological band insulators and topological superconductors. Starting from a Chern insulator, the concepts of topological band theory and the bulk boundary corre- spondence are explained. It is then shown that the low energy Hamiltonian of mercury telluride (HgTe) quantum wells of an appropriate thickness can be written as two time reversal symmetric copies of a Chern insulator. This leads to the quantum spin Hall effect. In such a system, spin-polarized one dimensional conducting states form at the edges of the material, while the bulk is insulating. This concept is extended to 3D topological insulators with conducting 2D surface states. As a preliminary step to treating topological superconductivity, a short review of the microscopic theory of superconductivity, i.e. the theory of Bardeen, Cooper, and Shrieffer (BCS theory) is presented. The presence of Majorana end modes in a one dimensional superconducting chain is explained using the Kitaev model. Finally, topological band insulators and conventional superconductivity are combined to effectively engineer p-wave superconductivity. One way to investigate these states is by measuring the periodicity of the phase of the Josephson supercurrent in a topological Josephson junction. The signature is a 4π-periodicity compared to the 2π-periodicity in conventional Josephson junctions. The proof of the presence of this effect in HgTe based Josephson junction is the main goal of this thesis and is discussed in chapters 3 to 6. Chapter 3 describes in detail the transport of a 3D topological insulator based weak link under radio-frequency radiation. The chapter starts with a review of the state of research of (i) strained HgTe as 3D topological insulator and (ii) the progress of induc- ing superconducting correlations into the topological surface states and the theoretical predictions of 3D TI based Josephson junctions. Josephson junctions based on strained HgTe are successfully fabricated. Before studying the ac driven Josephson junctions, the dc transport of the devices is analysed. The critical current as a function of temperature is measured and it is possible to determine the induced superconducting gap. Under rf illumination Shapiro steps form in the current voltage characteristic. A missing first step at low frequencies and low powers is found in our devices. This is a signature of a 4π-periodic supercurrent. By studying the device in a wide parameter range - as a 147148 SUMMARY function of frequency, power, device geometry and magnetic field - it is shown that the results are in agreement with the presence of a single gapless Andreev doublet and several conventional modes. Chapter 4 gives results of the numerical modelling of the I -V dynamics in a Josephson junction where both a 2π- and a 4π-periodic supercurrents are present. This is done in the framework of an equivalent circuit representation, namely the resistively shunted Josephson junction model (RSJ-model). The numerical modelling is in agreement with the experimental results in chapter 3. First, the missing of odd Shapiro steps can be understood by a small 4π-periodic supercurrent contribution and a large number of modes which have a conventional 2π-periodicity. Second, the missing of odd Shapiro steps occurs at low frequency and low rf power. Third, it is shown that stochastic processes like Landau Zener tunnelling are most probably not responsible for the 4π contribution. In a next step the periodicity of Josephson junctions based on quantum spin Hall insulators using are investigated in chapter 5. A fabrication process of Josephson junctions based on inverted HgTe quantum wells was successfully developed. In order to achieve a good proximity effect the barrier material was removed and the superconductor deposited without exposing the structure to air. In a next step a gate electrode was fabricated which allows the chemical potential of the quantum well to be tuned. The measurement of the diffraction pattern of the critical current Ic due to a magnetic field applied perpendicular to the sample plane was conducted. In the vicinity to the expected quantum spin Hall phase, the pattern resembles that of a superconducting quantum interference device (SQUID). This shows that the current flows predominantly on the edges of the mesa. This observation is taken as a proof of the presence of edge currents. By irradiating the sample with rf, missing odd Shapiro steps up to step index n = 9 have been observed. This evidences the presence of a 4π-periodic contribution to the supercurrent. The experiment is repeated using a weak link based on a non-inverted HgTe quantum well. This material is expected to be a normal band insulator without helical edge channels. In this device, all the expected Shapiro steps are observed even at low frequencies and over the whole gate voltage range. This shows that the observed phenomena are directly connected to the topological band structure. Both features, namely the missing of odd Shapiro steps and the SQUID like diffraction pattern, appear strongest towards the quantum spin Hall regime, and thus provide evidence for induced topological superconductivity in the helical edge states. A more direct way to probe the periodicity of the Josephson supercurrent than using Shapiro steps is the measurement of the emitted radiation of a weak link. This experiment is presented in chapter 6. A conventional Josephson junction converts a dc bias V to an ac current with a characteristic Josephson frequency fJ = eV /h. In a topological Josephson junction a frequency at half the Josephson frequency fJ /2 is expected. A new measurement setup was developed in order to measure the emitted spectrum of a single Josephson junction. With this setup the spectrum of a HgTe quantum well based Josephson junction was measured and the emission at half the Josephson frequency fJ /2 was detected. In addition, fJ emission is also detected depending on the gate voltage and detection frequency. The spectrum is again dominated by half the Josephson emission at low voltages while the conventional emission is determines the spectrum at high voltages. A non-inverted quantum well shows only conventional emission over the whole gateSUMMARY 149 voltage and frequency range. The linewidth of the detected frequencies gives a measure on the lifetime of the bound states: From there, a coherence time of 0.3-4ns for the fJ /2 line has been deduced. This is generally shorter than for the fJ line (3-4ns). The last part of the thesis, chapter 7, reports on the induced superconducting state in a strained HgTe layer investigated by point-contact Andreev reflection spectroscopy. For the experiment, a HgTe mesa was fabricated with a small constriction. The diameter of the orifice was chosen to be smaller than the mean free path estimated from magne- totransport measurements. Thus one gets a ballistic point-contact which allows energy resolved spectroscopy. One part of the mesa is covered with a superconductor which induces superconducting correlations into the surface states of the topological insulator. This experiment therefore probes a single superconductor normal interface. In contrast to the Josephson junctions studied previously, the geometry allows the acquisition of energy resolved information of the induced superconducting state through the measurement of the differential conductance dI/dV as a function of applied dc bias for various gate voltages, temperatures and magnetic fields. An induced superconducting order parame- ter of about 70µeV was extracted but also signatures of the niobium gap at the expected value around Δ Nb ≈ 1.1meV have been found. Simulations using the theory developed by Blonder, Tinkham and Klapwijk and an extended model taking the topological surface states into account were used to fit the data. The simulations are in agreement with a small barrier at the topological insulator-induced topological superconductor interface and a high barrier at the Nb to topological insulator interface. To understand the full con- ductance curve as a function of applied voltage, a non-equilibrium driven transformation is suggested. The induced superconductivity is suppressed at a certain bias value due to local electron population. In accordance with this suppression, the relevant scattering regions change spatially as a function of applied bias. To conclude, it is emphasized that the experiments conducted in this thesis found clear signatures of induced topological superconductivity in HgTe based quantum well and bulk devices and opens up the avenue to many experiments. It would be interesting to apply the developed concepts to other topological matter-superconductor hybrid systems. The direct spectroscopy and manipulation of the Andreev bound states using circuit quantum electrodynamic techniques should be the next steps for HgTe based samples. This was already achieved in superconducting atomic break junctions by the group in Saclay [Science 2015, 349, 1199-1202 (2015)]. Another possible development would be the on-chip detection of the emitted spectrum as a function of the phase φ through the junction. In this connection, the topological junction needs to be shunted by a parallel ancillary junction. Such a setup would allow the current phase relation I(φ) directly and the lifetime of the bound states to be measured directly. By coupling this system to a spectrometer, which can be another Josephson junction, the energy dependence of the Andreev bound states E(φ) could be obtained. The experiments on the Andreev reflection spectroscopy described in this thesis could easily be extended to two dimensional topological insulators and to more complex geometries, like a phase bias loop or a tunable barrier at the point-contact. This work might also be useful for answering the question how and why Majorana bound states can be localized in quantum spin Hall systems.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{Grauer2018,
  author    = {Grauer, Stefan},
  title     = {Transport Phenomena in Bi\(_2\)Se\(_3\) and Related Compounds},
  publisher = {Verlag Dr. Hut GmbH},
  isbn      = {978-3-8439-3481-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-157666},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2018},
  abstract  = {One of the most significant technological advances in history was driven by the utilization of a new material class: semiconductors. Its most important application being the transistor, which is indispensable in our everyday life. The technological advance in the semiconductor industry, however, is about to slow down. Making transistors ever smaller to increase the performance and trying to reduce and deal with the dissipative heat will soon reach the limits dictated by quantum mechanics with Moore himself, predicting the death of his famous law in the next decade. A possible successor for semiconductor transistors is the recently discovered material class of topological insulators. A material which in its bulk is insulating but has topological protected metallic surface states or edge states at its boundary. Their electrical transport characteristics include forbidden backscattering and spin-momentum-locking with the spin of the electron being perpendicular to its momentum. Topological insulators therefore offer an opportunity for high performance devices with low dissipation, and applications in spintronic where data is stored and processed at the same point. The topological insulator Bi\(_2\)Se\(_3\) and related compounds offer relatively high energy band gaps and a rather simple band structure with a single dirac cone at the gamma point of the Brillouin zone. These characteritics make them ideal candidates to study the topological surface state in electrical transport experiments and explore its physics.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{AlBaidhani2018,
  author    = {Al-Baidhani, Mohammed},
  title     = {Spectroscopy as a tool to investigate the high energy optical properties of nanostructured magnetically doped topological insulator},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-157221},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2018},
  abstract  = {In this dissertation the electronic and high-energy optical properties of thin nanoscale films of the magnetic topological insulator (MTI) (V,Cr)y(BixSb1-x)2-yTe3 are studied by means of X-ray photoelectron spectroscopy (XPS) and electron energy-loss spectroscopy (EELS). Magnetic topological insulators are presently of broad interest as the combination of ferromagnetism and spin-orbit coupling in these materials leads to a new topological phase, the quantum anomalous Hall state (QAHS), with dissipation less conduction channels. Determining and controlling the physical properties of these complex materials is therefore desirable for a fundamental understanding of the QAHS and for their possible application in spintronics. EELS can directly probe the electron energy-loss function of a material from which one can obtain the complex dynamic dielectric function by means of the Kramers-Kronig transformation and the Drude-Lindhard model of plasmon oscillations. The XPS core-level spectra in (V,Cr)y(BixSb1-x)2-yTe3 are analyzed in detail with regards to inelastic background contributions. It is shown that the spectra can be accurately described based on the electron energy-loss function obtained from an independent EELS measurement. This allows for a comprehensive and quantitative analysis of the XPS data, which will facilitate future core-level spectroscopy studies in this class of topological materials. From the EELS data, furthermore, the bulk and surface optical properties were estimated, and compared to ab initio calculations based on density functional theory (DFT) performed in the GW approximation for Sb2Te3. The experimental results show a good agreement with the calculated complex dielectric function and the calculated energy-loss function. The positions of the main plasmon modes reported here are expected to be generally similar in other materials in this class of nanoscale TI films. Hence, the present work introduces EELS as a powerful method to access the high-energy optical properties of TI thin films. Based on the presented results it will be interesting to explore more systematically the effects of stoichiometry, magnetic doping, film thickness and surface morphology on the electron-loss function, potentially leading to a better understanding of the complex interplay of structural, electronic, magnetic and optical properties in MTI nanostructures.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Geissler2017,
  author    = {Geißler, Florian},
  title     = {Transport properties of helical Luttinger liquids},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-153450},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2017},
  abstract  = {The prediction and the experimental discovery of topological insulators has set the stage for a novel type of electronic devices. In contrast to conventional metals or semiconductors, this new class of materials exhibits peculiar transport properties at the sample surface, as conduction channels emerge at the topological boundaries of the system. In specific materials with strong spin-orbit coupling, a particular form of a two-dimensional topological insulator, the quantum spin Hall state, can be observed. Here, the respective one-dimensional edge channels are helical in nature, meaning that there is a locking of the spin orientation of an electron and its direction of motion. Due to the symmetry of time-reversal, elastic backscattering off interspersed impurities is suppressed in such a helical system, and transport is approximately ballistic. This allows in principle for the realization of novel energy-efficient devices, ``spintronic`` applications, or the formation of exotic bound states with non-Abelian statistics, which could be used for quantum computing. The present work is concerned with the general transport properties of one-dimensional helical states. Beyond the topological protection mentioned above, inelastic backscattering can arise from various microscopic sources, of which the most prominent ones will be discussed in this Thesis. As it is characteristic for one-dimensional systems, the role of electron-electron interactions can be of major importance in this context. First, we review well-established techniques of many-body physics in one dimension such as perturbative renormalization group analysis, (Abelian) bosonization, and Luttinger liquid theory. The latter allow us to treat electron interactions in an exact way. Those methods then are employed to derive the corrections to the conductance in a helical transport channel, that arise from various types of perturbations. Particularly, we focus on the interplay of Rashba spin-orbit coupling and electron interactions as a source of inelastic single-particle and two-particle backscattering. It is demonstrated, that microscopic details of the system, such as the existence of a momentum cutoff, that restricts the energy spectrum, or the presence of non-interacting leads attached to the system, can fundamentally alter the transport signature. By comparison of the predicted corrections to the conductance to a transport experiment, one can gain insight about the microscopic processes and the structure of a quantum spin Hall sample. Another important mechanism we analyze is backscattering induced by magnetic moments. Those findings provide an alternative interpretation of recent transport measurements in InAs/GaSb quantum wells.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Leubner2017,
  author    = {Leubner, Philipp},
  title     = {Strain-engineering of the Topological Insulator HgTe},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-152446},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2017},
  abstract  = {The subject of this thesis is the control of strain in HgTe thin-film crystals. Such systems are members of the new class of topological insulator materials and therefore of special research interest. A major task was the experimental control of the strain in the HgTe films. This was achieved by a new epitaxial approach and confirmed by cristallographic analysis and magneto-transport measurements. In this work, strain was induced in thin films by means of coherent epitaxy on substrate crystals. This means that the film adopts the lattice constant of the substrate in the plane of the substrate-epilayer interface. The level of strain is determined by the difference between the strain-free lattice constants of the substrate and epilayer material (the so-called lattice mismatch). The film responds to an in-plane strain with a change of its lattice constant perpendicular to the interface. This relationship is crucial for both the correct interpretation of high resolution X-ray diffraction (HRXRD) measurements, and the precise determination of the band dispersion. The lattice constant of HgTe is smaller than the lattice constant of CdTe. Therefore, strain in HgTe is tensile if it is grown on a CdTe substrate. In principle, compressive strain can be achieved by using an appropriate \(\text{Cd}_{1-x}\text{Zn}_{x}\text{Te}\) substrate. This concept was modified and applied in this work. Epilayers have been fabricated by molecular-beam epitaxy (MBE). The growth of thick buffer layers of CdTe on GaAs:Si was established as an alternative to commercial CdTe and \(text{Cd}_{0.96}\text{Zn}_{0.04}\text{Te}\) substrates. The growth conditions have been optimized by an analysis of atomic force microscopy and HRXRD studies. HRXRD measurements reveal a power-law increase of the crystal quality with increasing thickness. Residual strain was found in the buffer layers, and was attributed to a combination of finite layer thickness and mismatch of the thermal expansion coefficients of CdTe and GaAs. In order to control the strain in HgTe epilayers, we have developed a new type of substrate with freely adjustable lattice constant. CdTe-\(\text{Cd}_{0.5}\text{Zn}_{0.5}\text{Te}\) strained-layer-superlattices have been grown by a combination of MBE and atomic-layer epitaxy (ALE), and have been analyzed by HRXRD. ALE of the \(\text{Cd}_{0.5}\text{Zn}_{0.5}\text{Te}\) layer is self-limiting to one monolayer, and the effective lattice constant can be controlled reproducibly and straightforward by adjusting the CdTe layer thickness. The crystal quality has been found to degrade with increasing Zn-fraction. However, the effect is less drastic compared to single layer \(\text{Cd}_{1-x}\text{Zn}_{x}\text{Te}\) solid solutions. HgTe quantum wells (QWs) sandwiched in between CdHgTe barriers have been fabricated in a similar fashion on superlattices and conventional CdTe and \(\text{Cd}_{0.96}\text{Zn}_{0.04}\text{Te}\) substrates. The lower critical thickness of the CdHgTe barrier material grown on superlattice substrates had to be considered regarding the sample design. The electronic properties of the QWs depend on the strain and thickness of the QW. We have determined the QW thickness with an accuracy of \(\pm\)0.5 nm by an analysis of the beating patterns in the thickness fringes of HRXRD measurements and X-ray reflectometry measurements. We have, for the first time, induced compressive strain in HgTe QWs by an epitaxial technique (i.e. the effective lattice constant of the superlattice is lower compared to the lattice constant of HgTe). The problem of the lattice mismatch between superlattice and barriers has been circumvented by using CdHgTe-ZnHgTe superlattices instead of CdHgTe as a barrier material. Furthermore, the growth of compressively strained HgTe bulk layers (with a thickness of at least 50 nm) was demonstrated as well. The control of the state of strain adds a new degree of freedom to the design of HgTe epilayers, which has a major influence on the band structure of QWs and bulk layers. Strain in bulk layers lifts the degeneracy of the \(\Gamma_8\) bands at \(\mathbf{k}=0\). Tensile strain opens an energy gap, compressive strain shifts the touching points of the valence- and conduction band to positions in the Brillouin zone with finite \(\mathbf{k}\). Such a situation has been realized for the first time in the course of this work. For QWs in the inverted regime, it is demonstrated that compressive strain can be used to significantly enhance the thermal energy gap of the two-dimensional electron gas (2DEG). In addition, semi-metallic and semiconducting behavior is expected in wide QWs, depending on the state of strain. An examination of the temperature dependence of the subband ordering in QWs revealed that the band gap is only temperature-stable for appropriate sample parameters and temperature regimes. The band inversion is always lifted for sufficiently high temperatures. A large number of models investigate the influence of the band gap on the stability of the quantum-spin-Hall (QSH) effect. An enhancement of the stability of QSH edge state conductance is expected for enlarged band gaps. Furthermore, experimental studies on the temperature dependence of the QSH conductance are in contradiction to theoretical predictions. Systematic studies of these aspects have become feasible based on the new flexibility of the sample design. Detailed low-temperature magnetotransport studies have been carried out on QWs and bulk layers. For this purpose, devices have been fabricated lithographically, which consist of two Hall-bar geometries with different dimensions. This allows to discriminate between conductance at the plane of the 2DEG and the edge of the sample. The Fermi energy in the 2DEG has been adjusted by means of a top gate electrode. The strain-induced transition from semi-metallic to semiconducting characteristics in wide QWs was shown. The magnitude of the semi-metallic overlap of valence- and conduction band was determined by an analysis of the two-carrier conductance and is in agreement with band structure calculations. The band gap of the semiconducting sample was determined by measurements of the temperature dependence of the conductance at the charge-neutrality point. Agreement with the value expected from theory has been achieved for the first time in this work. The influence of the band gap on the stability of QSH edge state conductance has been investigated on a set of six samples. The band gap of the set spans a range of 10 to 55 meV. The latter value has been achieved in a highly compressively strained QW, has been confirmed by temperature-dependent conductance measurements, and is the highest ever reported in the inverted regime. Studies of the carrier mobility reveal a degradation of the sample quality with increasing Zn-fraction in the superlattice, in agreement with HRXRD observations. The enhanced band gap does not suppress scattering mechanisms in QSH edge channels, but lowers the conductance in the plane of the 2DEG. Hence, edge state conductance is the dominant conducting process even at elevated temperatures. An increase in conductance with increasing temperature has been found, in agreement with reports from other groups. The increase follows a power-law dependency, the underlying physical mechanism remains open. A cause for the lack of an increase of the QSH edge state conductance with increasing energy gap has been discussed. Possibly, the sample remains insulating even at finite carrier densities, due to localization effects. The measurement does not probe the QSH edge state conductance at the situation where the Fermi energy is located in the center of the energy gap, but in the regime of maximized puddle-driven scattering. In a first set of measurements, it has been shown that the QSH edge state conductance can be influenced by hysteretic charging effects of trapped states in the insulating dielectric. A maximized conductance of \(1.6\ \text{e}^2/\text{h}\) was obtained in a \(58\ \mu\text{m}\) edge channel. Finally, measurements on three dimensional samples have been discussed. Recent theoretical works assign compressively strained HgTe bulk layers to the Weyl semi-metal class of materials. Such layers have been synthesized and studied in magnetotransport experiments for the first time. Pronounced quantum-Hall- and Shubnikov-de-Haas features in the Hall- and longitudinal resistance indicate two-dimensional conductance on the sample surface. However, this conductance cannot be assigned definitely to Weyl surface states, due to the inversion of \(\Gamma_6\) and \(\Gamma_8\) bands. If a magnetic field is aligned parallel to the current in the device, a decrease in the longitudinal resistance is observed with increasing magnetic field. This is a signature of the chiral anomaly, which is expected in Weyl semi-metals.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{Juergens2017,
  author    = {J{\"u}rgens, Stefan},
  title     = {Correlated Topological Materials},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-152202},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2017},
  abstract  = {The topic of this PhD thesis is the combination of topologically non-trivial phases with correlation effects stemming from Coulomb interaction between the electrons in a condensed matter system. Emphasis is put on both emerging benefits as well as hindrances, e.g. concerning the topological protection in the presence of strong interactions. The physics related to topological effects is established in Sec. 2. Based on the topological band theory, we introduce topological materials including Chern insulators, topological insulators in two and three dimensions as well as Weyl semimetals. Formalisms for a controlled treatment of Coulomb correlations are presented in Sec. 3, starting with the topological field theory. The Random Phase Approximation is introduced as a perturbative approach, while in the strongly interacting limit the theory of quantum Hall ferromagnetism applies. Interactions in one dimension are special, and are treated through the Luttinger liquid description. The section ends with an overview of the expected benefits offered by the combination of topology and interactions, see Sec. 3.3. These ideas are then elaborated in the research part. In Chap. II, we consider weakly interacting 2D topological insulators, described by the Bernevig-Hughes-Zhang model. This is applicable, e.g., to quantum well structures made of HgTe/CdTe or InAs/GaSb. The bulk band structure is here a mixture stemming from linear Dirac and quadratic Schr{\"o}dinger fermions. We study the low-energy excitations in Random Phase Approximation, where a new interband plasmon emerges due to the combined Dirac and Schr{\"o}dinger physics, which is absent in the separate limits. Already present in the undoped limit, one finds it also at finite doping, where it competes with the usual intraband plasmon. The broken particle-hole symmetry in HgTe quantum wells allows for an effective separation of the two in the excitation spectrum for experimentally accessible parameters, in the right range for Raman or electron loss spectroscopy. The interacting bulk excitation spectrum shows here clear differences between the topologically trivial and topologically non-trivial regime. An even stronger signal in experiments is expected from the optical conductivity of the system. It thus offers a quantitative way to identify the topological phase of 2D topological insulators from a bulk measurement. In Chap. III, we study a strongly interacting system, forming an ordered, quantum Hall ferromagnetic state. The latter can arise also in weakly interacting materials with an applied strong magnetic field. Here, electrons form flat Landau levels, quenching the kinetic energy such that Coulomb interaction can be dominant. These systems define the class of quantum Hall topological insulators: topologically non-trivial states at finite magnetic field, where the counter-propagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. Possible material realizations are 2D topological insulators like HgTe heterostructures and graphene. In our analysis, we focus on the vicinity of the topological phase transition, where the system is in a strongly interacting quantum Hall ferromagnetic state. The bulk and edge physics can be described by a nonlinear \sigma-model for the collective order parameter of the ordered state. We find that an emerging, continuous U(1) symmetry offers topological protection. If this U(1) symmetry is preserved, the topologically non-trivial phase persists in the presence of interactions, and we find a helical Luttinger liquid at the edge. The latter is highly tunable by the magnetic field, where the effective interaction strength varies from weakly interacting at zero field, K \approx 1, to diverging interaction strength at the phase transition, K -> 0. In the last Chap. IV, we investigate whether a Weyl semimetal and a 3D topological insulator phase can exist together at the same time, with a combined, hybrid surface state at the joint boundaries. An overlap between the two can be realized by Coulomb interaction or a spatial band overlap of the two systems. A tunnel coupling approach allows us to derive the hybrid surface state Hamiltonian analytically, enabling a detailed study of its dispersion relation. For spin-symmetric coupling, new Dirac nodes emerge out of the combination of a single Dirac node and a Fermi arc. Breaking the spin symmetry through the coupling, the dispersion relation is gapped and the former Dirac node gets spin-polarized. We propose experimental realizations of the hybrid physics, including compressively strained HgTe as well as heterostructures of topological insulator and Weyl semimetal materials, connected to each other, e.g., by Coulomb interaction.},
  subject      = {Topologie},
  language  = {en}
}
@phdthesis{Ames2015,
  author    = {Ames, Christopher},
  title     = {Molecular Beam Epitaxy of 2D and 3D HgTe, a Topological Insulator},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-151136},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {In the present thesis the MBE growth and sample characterization of HgTe structures is investigated and discussed. Due to the first experimental discovery of the quantum Spin Hall effect (QSHE) in HgTe quantum wells, this material system attains a huge interest in the spintronics society. Because of the long history of growing Hg-based heterostructures here at the Experimentelle Physik III in W{\"u}rzburg, there are very good requirements to analyze this material system more precisely and in new directions. Since in former days only doped HgTe quantum wells were grown, this thesis deals with the MBE growth in the (001) direction of undoped HgTe quantum wells, surface located quantum wells and three dimensional bulk layers. All Hg-based layers were grown on CdTe substrates which generate strain in the layer stack and provide therefore new physical effects. In the same time, the (001) CdTe growth was investigated on n-doped (001) GaAs:Si because the Japanese supplier of CdTe substrates had a supply bottleneck due to the Tohoku earthquake and its aftermath in 2011. After a short introduction of the material system, the experimental techniques were demonstrated and explained explicitly. After that, the experimental part of this thesis is displayed. So, the investigation of the (001) CdTe growth on (001) GaAs:Si is discussed in chapter 4. Firstly, the surface preparation of GaAs:Si by oxide desorption is explored and analyzed. Here, rapid thermal desorption of the GaAs oxide with following cool down in Zn atmosphere provides the best results for the CdTe due to small holes at the surface, while e.g. an atomic flat GaAs buffer deteriorates the CdTe growth quality. The following ZnTe layer supplies the (001) growth direction of the CdTe and exhibits best end results of the CdTe for 30 seconds growth time at a flux ratio of Zn/Te ~ 1/1.2. Without this ZnTe layer, CdTe will grow in the (111) direction. However, the main investigation is here the optimization of the MBE growth of CdTe. The substrate temperature, Cd/Te flux ratio and the growth time has to be adjusted systematically. Therefore, a complex growth process is developed and established. This optimized CdTe growth process results in a RMS roughness of around 2.5 nm and a FWHM value of the HRXRD w-scan of 150 arcsec. Compared to the literature, there is no lower FWHM value traceable for this growth direction. Furthermore, etch pit density measurements show that the surface crystallinity is matchable with the commercial CdTe substrates (around 1x10^4 cm^(-2)). However, this whole process is not completely perfect and offers still room for improvements. The growth of undoped HgTe quantum wells was also a new direction in research in contrast to the previous n-doped grown HgTe quantum wells. Here in chapter 5, the goal of very low carrier densities was achieved and therefore it is now possible to do transport experiments in the n - and p - region by tuning the gate voltage. To achieve this high sample quality, very precise growth of symmetric HgTe QWs and their HRXRD characterization is examined. Here, the quantum well thickness can now determined accurate to under 0.3 nm. Furthermore, the transport analysis of different quantum well thicknesses shows that the carrier density and mobility increase with rising HgTe layer thickness. However, it is found out that the band gap of the HgTe QW closes indirectly at a thickness of 11.6 nm. This is caused by the tensile strained growth on CdTe substrates. Moreover, surface quantum wells are studied. These quantum wells exhibit no or a very thin HgCdTe cap. Though, oxidization and contamination of the surface reduces here the carrier mobility immensely and a HgCdTe layer of around 5 nm provides the pleasing results for transport experiments with superconductors connected to the topological insulator [119]. A completely new achievement is the realization of MBE growth of HgTe quantum wells on CdTe/GaAs:Si substrates. This is attended by the optimization of the CdTe growth on GaAs:Si. It exposes that HgTe quantum wells grown in-situ on optimized CdTe/GaAs:Si show very nice transport data with clear Hall plateaus, SdH oscillations, low carrier densities and carrier mobilities up to 500 000 cm^2/Vs. Furthermore, a new oxide etching process is developed and analyzed which should serve as an alternative to the standard HCl process which generates volcano defects at some time. However, during the testing time the result does not differ in Nomarski, HRXRD, AFM and transport measurements. Here, long-time tests or etching and mounting in nitrogen atmosphere may provide new elaborate results. The main focus of this thesis is on the MBE growth and standard characterization of HgTe bulk layers and is discussed in chapter 6. Due to the tensile strained growth on lattice mismatched CdTe, HgTe bulk opens up a band gap of around 22 meV at the G-point and exhibits therefore its topological surface states. The analysis of surface condition, roughness, crystalline quality, carrier density and mobility via Nomarski, AFM, XPS, HRXRD and transport measurements is therefore included in this work. Layer thickness dependence of carrier density and mobility is identified for bulk layer grown directly on CdTe substrates. So, there is no clear correlation visible between HgTe layer thickness and carrier density or mobility. So, the carrier density is almost constant around 1x10^11 cm^(-2) at 0 V gate voltage. The carrier mobility of these bulk samples however scatters between 5 000 and 60 000 cm^2/Vs almost randomly. Further experiments should be made for a clearer understanding and therefore the avoidance of unusable bad samples.But, other topological insulator materials show much higher carrier densities and lower mobility values. For example, Bi2Se3 exhibits just density values around 1019 cm^(-2) and mobility values clearly below 5000 cm2/Vs. The carrier density however depends much on lithography and surface treatment after growth. Furthermore, the relaxation behavior and critical thickness of HgTe grown on CdTe is determined and is in very good agreement with theoretical prediction (d_c = 155 nm). The embedding of the HgTe bulk layer between HgCdTe layers created a further huge improvement. Similar to the quantum well structures the carrier mobility increases immensely while the carrier density levels at around 1x10^11 cm^(-2) at 0 V gate voltage as well. Additionally, the relaxation behavior and critical thickness of these barrier layers has to be determined. HgCdTe grown on commercial CdTe shows a behavior as predicted except the critical thickness which is slightly higher than expected (d_c = 850 nm). Otherwise, the relaxation of HgCdTe grown on CdTe/GaAs:Si occurs in two parts. The layer is fully strained up to 250 nm. Between 250 nm and 725 nm the HgCdTe film starts to relax randomly up to 10 \%. The relaxation behavior for thicknesses larger than 725 nm occurs than linearly to the inverse layer thickness. A explanation is given due to rough interface conditions and crystalline defects of the CdTe/GaAs:Si compared to the commercial CdTe substrate. HRXRD and AFM data support this statement. Another point is that the HgCdTe barriers protect the active HgTe layer and because of the high carrier mobilities the Hall measurements provide new transport data which have to be interpreted more in detail in the future. In addition, HgTe bulk samples show very interesting transport data by gating the sample from the top and the back. It is now possible to manipulate the carrier densities of the top and bottom surface states almost separately. The back gate consisting of the n-doped GaAs substrate and the thick insulating CdTe buffer can tune the carrier density for Delta(n) ~ 3x10^11 cm^(-2). This is sufficient to tune the Fermi energy from the p-type into the n-type region [138]. In this thesis it is shown that strained HgTe bulk layers exhibit superior transport data by embedding between HgCdTe barrier layers. The n-doped GaAs can here serve as a back gate. Furthermore, MBE growth of high crystalline, undoped HgTe quantum wells shows also new and extended transport output. Finally, it is notable that due to the investigated CdTe growth on GaAs the Hg-based heterostructure MBE growth is partially independent from commercial suppliers.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{Kessel2016,
  author    = {Kessel, Maximilian},
  title     = {HgTe shells on CdTe nanowires: A low-dimensional topological insulator from crystal growth to quantum transport},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-149069},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {A novel growth method has been developed, allowing for the growth of strained HgTe shells on CdTe nanowires (NWs). The growth of CdTe-HgTe core-shell NWs required high attention in controlling basic parameters like substrate temperature and the intensity of supplied material fluxes. The difficulties in finding optimized growth conditions have been successfully overcome in this work. We found the lateral redistribution of liquid growth seeds with a ZnTe growth start to be crucial to trigger vertical CdTe NW growth. Single crystalline zinc blende CdTe NWs grew, oriented along [111]B. The substrate temperature was the most critical parameter to achieve straight and long wires. In order to adjust it, the growth was monitored by reflection high-energy electron diffraction, which was used for fine tuning of the temperature over time in each growth run individually. For optimized growth conditions, a periodic diffraction pattern allowed for the detailed analysis of atomic arrangement on the surfaces and in the bulk. The ability to do so reflected the high crystal quality and ensemble uniformity of our CdTe NWs. The NW sides were formed by twelve stable, low-index crystalline facets. We observed two types stepped and polar sides, separated by in total six flat and non-polar facets. The high crystalline quality of the cores allowed to grow epitaxial HgTe shells around. We reported on two different heterostructure geometries. In the first one, the CdTe NWs exhibit a closed HgTe shell, while for the second one, the CdTe NWs are overgrown mainly on one side. Scanning electron microscopy and scanning transmission electron microscopy confirmed, that many of the core-shell NWs are single crystalline zinc blende and have a high uniformity. The symmetry of the zinc blende unit cell was reduced by residual lattice strain. We used high-resolution X-ray diffraction to reveal the strain level caused by the small lattice mismatch in the heterostructures. Shear strain has been induced by the stepped hetero-interface, thereby stretching the lattice of the HgTe shell by 0.06 \% along a direction oriented with an angle of 35 ° to the interface. The different heterostructures obtained, were the base for further investigation of quasi-one-dimensional crystallites of HgTe. We therefore developed methods to reliably manipulate, align, localize and contact individual NWs, in order to characterize the charge transport in our samples. Bare CdTe cores were insulating, while the HgTe shells were conducting. At low temperature we found the mean free path of charge carriers to be smaller, but the phase coherence length to be larger than the sample size of several hundred nanometers. We observed universal conductance fluctuations and therefore drew the conclusion, that the trajectories of charge carriers are defined by elastic backscattering at randomly distributed scattering sites. When contacted with superconducting leads, we saw induced superconductivity, multiple Andreev reflections and the associated excess current. Thus, we achieved HgTe/superconductor interfaces with high interfacial transparency. In addition, we reported on the appearance of peaks in differential resistance at Delta/e for HgTe-NW/superconductor and 2*Delta/e for superconductor/HgTe-NW/superconductor junctions, which is possibly related to unconventional pairing at the HgTe/superconductor interface. We noticed that the great advantage of our self-organized growth is the possibility to employ the metallic droplet, formerly seeding the NW growth, as a superconducting contact. The insulating wire cores with a metallic droplet at the tip have been overgrown with HgTe in a fully in-situ process. A very high interface quality was achieved in this case.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{Schreyeck2016,
  author    = {Schreyeck, Steffen},
  title     = {Molecular Beam Epitaxy and Characterization of Bi-Based V\(_2\)VI\(_3\) Topological Insulators},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-145812},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {The present thesis is addressed to the growth and characterization of Bi-based V2VI3 topological insulators (TIs). The TIs were grown by molecular beam epitaxy (MBE) on differently passivated Si(111) substrates, as well as InP(111) substrates. This allows the study of the influence of the substrate on the structural and electrical properties of the TIs. The Bi2Se3 layers show a change of mosaicity-tilt and -twist for growth on the differently prepared Si(111) substrates, as well as a significant increase of crystalline quality for growth on the lateral nearly lattice matched InP(111). The rocking curve FWHMs observed for thick layers grown on InP are comparable to these of common zincblende layers, which are close to the resolution limit of standard high resolution X-ray diffraction (HRXRD) setups. The unexpected high structural crystalline quality achieved in this material system is remarkable due to the presence of weak van der Waals bonds between every block of five atomic layers, i.e. a quintuple layer (QL), in growth direction. In addition to the mosaicity also twin domains, present in films of the V2VI3 material system, are studied. The twin defects are observed in Bi2Se3 layers grown on Si(111) and lattice matched InP(111) suggesting that the two dimensional surface lattice of the substrates can not determine the stacking order ABCABC... or ACBACB... in locally separated growth seeds. Therefore the growth on misoriented and rough InP(111) is analyzed. The rough InP(111) with its facets within a hollow exceeding the height of a QL is able to provide its stacking information to the five atomic layers within a QL. By varying the roughness of the InP substrate surface, due to thermal annealing, the influence on the twinning within the layer is confirmed resulting in a complete suppression of twin domains on rough InP(111). Focusing on the electrical properties of the Bi2Se3 films, the increased structural quality for films grown on lattice matched flat InP(111)B results in a marginal reduction of carrier density by about 10\% compared to the layers grown on H-passivated Si(111), whereas the suppression of twin domains for growth on rough InP(111)B resulted in a reduction of carrier density by an order of magnitude. This implies, that the twin domains are a main crystal defect responsible for the high carrier density in the presented Bi2Se3 thin films. Besides the binary Bi2Se3 also alloys with Sb and Te are fabricated to examine the influence of the compound specific point defects on the carrier density. Therefore growth series of the ternary materials Bi2Te(3-y)Se(y), Bi(2-x)Sb(x)Se3, and Bi(2-x)Sb(x)Te3, as well as the quaternary Bi(2-x)Sb(x)Te(3-y)Se(y) are studied. To further reduce the carrier density of twin free Bi2Se3 layers grown on InP(111)B:Fe a series of Bi(2-x)Sb(x)Se3 alloys were grown under comparable growth conditions. This results in a reduction of the carrier density with a minimum in the composition range of about x=0.9-1.0. The Bi(2-x)Sb(x)Te3 alloys exhibit a pn-transition, due to the dominating n-type and p-type point defects in its binary compounds, which is determined to reduce the bulk carrier density enabling the study the TI surface states. This pn-transition plays a significant role in realizing predicted applications and exotic effects, such as the quantum anomalous Hall effect. The magnetic doping of topological insulators with transition metals is studied by incorporating Cr and V in the alloy Bi(2-x)Sb(x)Te3 by codeposition. The preferential incorporation of Cr on group-V sites is confirmed by EDX and XRD, whereas the incorporation of Cr reduces the crystalline quality of the layer. Magnetotransport measurements of the Cr-doped TIs display an anomalous Hall effect confirming the realization of a magnetic TI thin film. The quantum anomalous Hall effect is observed in V-doped Bi(2-x)Sb(x)Te3, where the V-doping results in higher Curie temperatures, as well as higher coercive fields compared to the Cr-doping of the TIs. Moreover the present thesis contributes to the understanding of the role of the substrate concerning the crystalline quality of van der Waals bonded layers, such as the V2VI3 TIs, MoS2 and WoTe2. Furthermore, the fabrication of the thin film TIs Bi(2-x)Sb(x)Te(3-y)Se(y) in high crystalline quality serves as basis to explore the physics of topological insulators.},
  subject      = {Bismutverbindungen},
  language  = {en}
}
@phdthesis{Muehlbauer2015,
  author    = {M{\"u}hlbauer, Mathias Josef},
  title     = {Nanolithography on Mercury Telluride},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-137152},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Topological insulators belong to a new quantum state of matter that is currently one of the most recognized research fields in condensed matter physics. Strained bulk HgTe and HgTe/HgCdTe quantum well structures are currently one of few topological insulator material systems suitable to be studied in transport experiments. In addition HgTe quantum wells provide excellent requirements for the conduction of spintronic experiments. A fundamental requirement for most experiments, however, is to reliably pattern these heterostructures into advanced nano-devices. Nano-lithography on this material system proves to be challenging because of inherent temperature limitations, its high reactivity with various metals and due to its properties as a topological insulator. The current work gives an insight into why many established semiconductor lithography processes cannot be easily transferred to HgTe while providing alternative solutions. The presented developments include novel ohmic contacts, the prevention of metal sidewalls and redeposition fences in combination with low temperature (80 °C) lithography and an adapted hardmask lithography process utilizing a sacrificial layer. In addition we demonstrate high resolution low energy (2.5 kV) electron beam lithography and present an alternative airbridge gating technique. The feasibility of nano-structures on HgTe quantum wells is exemplarily verified in two separate transport experiments. We are first to realize physically etched quantum point contacts in HgTe/HgCdTe high mobility 2DEGs and to prove their controllability via external top-gate electrodes. So far quantum point contacts have not been reported in TI materials. However, these constrictions are part of many proposals to probe the nature of the helical quantum spin Hall edge channels and are suggested as injector and detector devices for spin polarized currents. To confirm their functionality we performed four-terminal measurements of the point contact conductance as a function of external gate voltage. Our measurements clearly exhibit quantized conductance steps in 2e2/h, which is a fundamental characteristic of quantum point contacts. Furthermore we conducted measurements on the formation and control of collimated electron beams, a key feature to realize an all electrical spin-optic device. In a second study several of the newly developed lithography techniques were implemented to produce arrays of nano-wires on inverted and non-inverted HgTe quantum well samples. These devices were used in order to probe and compare the weak antilocalization (WAL) in these structures as a function of magnetic field and temperature. Our measurements reveal that the WAL is almost an order of magnitude larger in inverted samples. This observation is attributed to the Dirac-like dispersion of the energy bands in HgTe quantum wells. The described lithography has already been successfully implemented and adapted in several published studies. All processes have been optimized to guarantee a minimum effect on the heterostructure's properties and the sample surface, which is especially important for probing the topological surface states of strained HgTe bulk layers. Our developments therefore serve as a base for continuous progress to further establish HgTe as a topological insulator and give access to new experiments.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Reinthaler2015,
  author    = {Reinthaler, Rolf Walter},
  title     = {Charge and Spin Transport in Topological Insulator Heterojunctions},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-135611},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Over the last decade, the field of topological insulators has become one of the most vivid areas in solid state physics. This novel class of materials is characterized by an insulating bulk gap, which, in two-dimensional, time-reversal symmetric systems, is closed by helical edge states. The latter make topological insulators promising candidates for applications in high fidelity spintronics and topological quantum computing. This thesis contributes to bringing these fascinating concepts to life by analyzing transport through heterostructures formed by two-dimensional topological insulators in contact with metals or superconductors. To this end, analytical and numerical calculations are employed. Especially, a generalized wave matching approach is used to describe the edge and bulk states in finite size tunneling junctions on the same footing. The numerical study of non-superconducting systems focuses on two-terminal metal/topological insulator/metal junctions. Unexpectedly, the conductance signals originating from the bulk and the edge contributions are not additive. While for a long junction, the transport is determined purely by edge states, for a short junction, the conductance signal is built from both bulk and edge states in a ratio, which depends on the width of the sample. Further, short junctions show a non-monotonic conductance as a function of the sample length, which distinguishes the topologically non-trivial regime from the trivial one. Surprisingly, the non-monotonic conductance of the topological insulator can be traced to the formation of an effectively propagating solution, which is robust against scalar disorder. The analysis of the competition of edge and bulk contributions in nanostructures is extended to transport through topological insulator/superconductor/topological insulator tunneling junctions. If the dimensions of the superconductor are small enough, its evanescent bulk modes can couple edge states at opposite sample borders, generating significant and tunable crossed Andreev reflection. In experiments, the latter process is normally disguised by simultaneous electron transmission. However, the helical edge states enforce a spatial separation of both competing processes for each Kramers' partner, allowing to propose an all-electrical measurement of crossed Andreev reflection. Further, an analytical study of the hybrid system of helical edge states and conventional superconductors in finite magnetic fields leads to the novel superconducting quantum spin Hall effect. It is characterized by edge states. Both the helicity and the protection against scalar disorder of these edge states are unaffected by an in-plane magnetic field. At the same time its superconducting gap and its magnetotransport signals can be tuned in weak magnetic fields, because the combination of helical edge states and superconductivity results in a giant g-factor. This is manifested in a non-monotonic excess current and peak splitting of the dI/dV characteristics as a function of the magnetic field. In consequence, the superconducting quantum spin Hall effect is an effective generator and detector for spin currents. The research presented here deepens the understanding of the competition of bulk and edge transport in heterostructures based on topological insulators. Moreover it proposes feasible experiments to all-electrically measure crossed Andreev reflection and to test the spin polarization of helical edge states.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Posske2015,
  author    = {Posske, Thore Hagen},
  title     = {Dressed Topological Insulators: Rashba Impurity, Kondo Effect, Magnetic Impurities, Proximity-Induced Superconductivity, Hybrid Systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-131249},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Topological insulators are electronic phases that insulate in the bulk and accommodate a peculiar, metallic edge liquid with a spin-dependent dispersion. They are regarded to be of considerable future use in spintronics and for quantum computation. Besides determining the intrinsic properties of this rather novel electronic phase, considering its combination with well-known physical systems can generate genuinely new physics. In this thesis, we report on such combinations including topological insulators. Specifically, we analyze an attached Rashba impurity, a Kondo dot in the two channel setup, magnetic impurities on the surface of a strong three-dimensional topological insulator, the proximity coupling of the latter system to a superconductor, and hybrid systems consisting of a topological insulator and a semimetal. Let us summarize our primary results. Firstly, we determine an analytical formula for the Kondo cloud and describe its possible detection in current correlations far away from the Kondo region. We thereby rely on and extend the method of refermionizable points. Furthermore, we find a class of gapless topological superconductors and semimetals, which accommodate edge states that behave similarly to the ones of globally gapped topological phases. Unexpectedly, we also find edge states that change their chirality when affected by sufficiently strong disorder. We regard the presented research helpful in future classifications and applications of systems containing topological insulators, of which we propose some examples.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Rothe2015,
  author    = {Rothe, Dietrich Gernot},
  title     = {Spin Transport in Topological Insulators and Geometrical Spin Control},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-125628},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {In the field of spintronics, spin manipulation and spin transport are the main principles that need to be implemented. The main focus of this thesis is to analyse semiconductor systems where high fidelity in these principles can be achieved. To this end, we use numerical methods for precise results, supplemented by simpler analytical models for interpretation. The material system of 2D topological insulators, HgTe/CdTe quantum wells, is interesting not only because it provides a topologically distinct phase of matter, physically manifested in its protected transport properties, but also since within this system, ballistic transport of high quality can be realized, with Rashba spin-orbit coupling and electron densities that are tunable by electrical gating. Extending the Bernvevig-Hughes-Zhang model for 2D topological insulators, we derive an effective four-band model including Rashba spin-orbit terms due to an applied potential that breaks the spatial inversion symmetry of the quantum well. Spin transport in this system shows interesting physics because the effects of Rashba spin-orbit terms and the intrinsic Dirac-like spin-orbit terms compete. We show that the resulting spin Hall signal can be dominated by the effect of Rashba spin-orbit coupling. Based on spin splitting due to the latter, we propose a beam splitter setup for all-electrical generation and detection of spin currents. Its working principle is similar to optical birefringence. In this setup, we analyse spin current and spin polarization signals of different spin vector components and show that large in-plane spin polarization of the current can be obtained. Since spin is not a conserved quantity of the model, we first analyse the transport of helicity, a conserved quantity even in presence of Rashba spin-orbit terms. The polarization defined in terms of helicity is related to in-plane polarization of the physical spin. Further, we analyse thermoelectric transport in a setup showing the spin Hall effect. Due to spin-orbit coupling, an applied temperature gradient generates a transverse spin current, i.e. a spin Nernst effect, which is related to the spin Hall effect by a Mott-like relation. In the metallic energy regimes, the signals are qualitatively explained by simple analytic models. In the insulating regime, we observe a spin Nernst signal that originates from the finite-size induced overlap of edge states. In the part on methods, we discuss two complementary methods for construction of effective semiconductor models, the envelope function theory and the method of invariants. Further, we present elements of transport theory, with some emphasis on spin-dependent signals. We show the connections of the adiabatic theorem of quantum mechanics to the semiclassical theory of electronic transport and to the characterization of topological phases. Further, as application of the adiabatic theorem to a control problem, we show that universal control of a single spin in a heavy-hole quantum dot is experimentally realizable without breaking time reversal invariance, but using a quadrupole field which is adiabatically changed as control knob. For experimental realization, we propose a GaAs/GaAlAs quantum well system.},
  subject      = {Elektronischer Transport},
  language  = {en}
}
@phdthesis{Thienel2015,
  author    = {Thienel, Cornelius},
  title     = {Exploring the transport properties of the three-dimensional topological insulator material HgTe},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-122031},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {In der vorliegenden Dissertation werden die Transporteigenschaften von verspannten HgTe-Volumenkristallen untersucht. Verspanntes HgTe stellt einen dreidimensionalen topologischen Isolator dar und ist zur Erkundung von topologischen Oberfl{\"a}chenzust{\"a}nden von speziellem Interesse, da es mit Hilfe von Molekularstrahlepitaxie in hoher Kristallqualit{\"a}t gewachsen werden kann. Die niedrige Defektdichte f{\"u}hrt zu beachtlichen Ladungstr{\"a}gerbeweglichkeiten, die deutlich {\"u}ber denen anderer topologischer Isolatoren liegen. Verspanntes HgTe hat jedoch eine kleine Energiel{\"u}cke von ca. 20 meV. Deshalb ist es f{\"u}r eine m{\"o}gliche Verwendung des Materials ein wichtiger Aspekt, in welchem Parameterbereich Oberfl{\"a}chentransport stattfindet. Um dieser Frage nachzugehen, werden die HgTe-Proben bei tiefen Temperaturen (T < 100 mK) und unter dem Einfluss hoher Magnetfelder in verschiedenen Orientierungen untersucht. Der Einfluss von Gate-Elektroden ober- und unterhalb der Struktur sowie von Deckschichten, die die Oberfl{\"a}chen sch{\"u}tzen, wird diskutiert. Basierend auf einer Analyse des Quanten-Hall-Effekts wird gezeigt, dass der Transport in diesem Material von topologischen Oberfl{\"a}chenzust{\"a}nden dominiert ist. Die Abh{\"a}ngigkeit der topologischen Oberfl{\"a}chenzust{\"a}nde von der Gate-Spannung wird dargestellt. Durch diese Abh{\"a}ngigkeit ist es zum ersten Mal m{\"o}glich, eine ungerade ganzzahlige Quanten-Hall-Plateau Sequenz nachzuweisen, die von den Oberfl{\"a}chen senkrecht zum Magnetfeld stammt. Des Weiteren wird im Rahmen dieser Arbeit in Proben hoher Oberfl{\"a}chenqualit{\"a}t zum ersten Mal f{\"u}r einen 3D TI der p-Typ QHE der Oberfl{\"a}chenzust{\"a}nde beobachtet. Aus der Gate-Abh{\"a}ngigkeit der Messungen wird geschlossen, dass das Abschirmverhalten in 3D TIs nicht trivial ist. Die Transportdaten werden mit Hilfe von intuitiven theoretischen Modellen auf qualitative Weise analysiert.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Maier2015,
  author    = {Maier, Luis},
  title     = {Induced superconductivity in the topological insulator mercury telluride},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-119405},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {The combination of a topological insulator (TI) and a superconductor (S), which together form a TI/S interface, is expected to influence the possible surface states in the TI. It is of special interest, if the theoretical prediction of zero energy Majorana states in this system is verifiable. This thesis presents the experimental realization of such an interface between the TI strained bulk HgTe and the S Nb and studies if the afore mentioned expectations are met. As these types of interfaces were produced for the first time the initial step was to develop a new lithographic process. Optimization of the S deposition technique as well as the application of cleaning processes allowed for reproducible fabrication of structures. In parallel the measurement setup was upgraded to be able to execute the sensitive measurements at low energy. Furthermore several filters have been implemented into the system to reduce high frequency noise and the magnetic field control unit was additionally replaced to achieve the needed resolution in the μT range. Two kinds of basic geometries have been studied: Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs). A JJ consists of two Nb contacts with a small separation on a HgTe layer. These S/TI/S junctions are one of the most basic structures possible and are studied via transport measurements. The transport through this geometry is strongly influenced by the behavior at the two S/TI interfaces. In voltage dependent differential resistance measurements it was possible to detect multiple Andreev reflections in the JJ, indicating that electrons and holes are able to traverse the HgTe gap between both interfaces multiple times while keeping phase coherence. Additionally using BTK theory it was possible to extract the interface transparency of several junctions. This allowed iterative optimization for the highest transparency via lithographic improvements at these interfaces. The increased transparency and thus the increased coupling of the Nb's superconductivity to the HgTe results in a deeper penetration of the induced superconductivity into the HgTe. Due to this strong coupling it was possible to enter the regime, where a supercurrent is carried through the complete HgTe layer. For the first time the passing of an induced supercurrent through strained bulk HgTe was achieved and thus opened the area for detailed studies. The magnetic dependence of the supercurrent in the JJ was recorded, which is also known as a Fraunhofer pattern. The periodicity of this pattern in magnetic field compared to the JJ geometry allowed to conclude how the junction depends on the phase difference between both superconducting contacts. Theoretical calculations predicted a phase periodicity of 4p instead of 2p, if a TI is used as weak link material between the contacts, due to the presence of Majorana modes. It could clearly be shown that despite the usage of a TI the phase still was 2p periodic. By varying further influencing factors, like number of modes and phase coherence length in the junction, it might still be possible to reach the 4p regime with bound Majorana states in the future. A good candidate for further experiments was found in capped HgTe samples, but here the fabrication process still has to be developed to the same quality as for the uncapped HgTe samples. The second type of geometry studied in this thesis was a DC-SQUID, which consists of two parallel JJs and can also be described as an interference device between two JJs. The DC-SQUID devices were produced in two configurations: The symmetric SQUID, where both JJs were identical, and the asymmetric SQUID, where one JJ was not linear, but instead has a 90° bent. These configurations allow to test, if the predicted uniformity of the superconducting band gap for induced superconductivity in a TI is valid. While the phase of the symmetric SQUID is not influenced by the shape of the band gap, the asymmetric SQUID would be in phase with the symmetric SQUID in case of an uniform band gap and out of phase if p- or d-wave superconductivity is dominating the transport, due to the 90° junction. As both devices are measured one after another, the problem of drift in the coil used to create the magnetic field has to be overcome in order to decide if the oscillations of both types of SQUIDs are in phase. With an oscillation period of 0.5 mT and a drift rate in the range of 5.5 μT/h the measurements on both configurations have to be conducted in a few hours. Only then the total shift is small enough to compare them with each other. For this to be possible a novel measurement system based on a real time micro controller was programmed, which allows a much faster extraction of the critical current of a device. The measurement times were reduced from days to hours, circumventing the drift problems and enabling the wanted comparison. After the final system optimizations it has been shown that the comparison should now be possible. Initial measurements with the old system hinted that both types of SQUIDs are in phase and thus the expected uniform band gap is more likely. With all needed optimizations in place it is now up to the successors of this project to conclusively prove this last point. This thesis has proven that it is possible to induce superconductivity in strained bulk HgTe. It has thus realized the most basic sample geometry proposed by Fu and Kane in 2008 for the appearance of Majorana bound states. Based on this work it is now possible to further explore induced superconductivity in strained bulk HgTe to finally reach a regime, where the Majorana states are both stable and detectable.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{Goth2015,
  author    = {Goth, Florian},
  title     = {Continuous time quantum Monte Carlo Studies of Quenches and Correlated Systems with Broken Inversion Symmetry},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-118836},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {This thesis deals with quantum Monte Carlo simulations of correlated low dimensional electron systems. The correlation that we have in mind is always given by the Hubbard type electron electron interaction in various settings. To facilitate this task, we develop the necessary methods in the first part. We develop the continuous time interaction expansion quantum algorithm in a manner suitable for the treatment of effective and non-equilibrium problems. In the second part of this thesis we consider various applications of the algorithms. First we examine a correlated one-dimensional chain of electrons that is subject to some form of quench dynamics where we suddenly switch off the Hubbard interaction. We find the light-cone-like Lieb-Robinson bounds and forms of restricted equilibration subject to the conserved quantities. Then we consider a Hubbard chain subject to Rashba spin-orbit coupling in thermal equilibrium. This system could very well be realized on a surface with the help of metallic adatoms. We find that we can analytically connect the given model to a model without spin-orbit coupling. This link enabled us to interpret various results for the standard Hubbard model, such as the single-particle spectra, now in the context of the Hubbard model with Rashba spin-orbit interaction. And finally we have considered a magnetic impurity in a host consisting of a topological insulator. We find that the impurity still exhibits the same features as known from the single impurity Anderson model. Additionally we study the effects of the impurity in the bath and we find that in the parameter regime where the Kondo singlet is formed the edge state of the topological insulator is rerouted around the impurity.},
  subject      = {Elektronenkorrelation},
  language  = {en}
}
@phdthesis{Bercx2014,
  author    = {Bercx, Martin Helmut},
  title     = {Numerical studies of heavy-fermion systems and correlated topological insulators},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-116138},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2014},
  abstract  = {In this thesis, we investigate aspects of the physics of heavy-fermion systems and correlated topological insulators. We numerically solve the interacting Hamiltonians that model the physical systems using quantum Monte Carlo algorithms to access both ground-state and finite-temperature observables. Initially, we focus on the metamagnetic transition in the Kondo lattice model for heavy fermions. On the basis of the dynamical mean-field theory and the dynamical cluster approximation, our calculations point towards a continuous transition, where the signatures of metamagnetism are linked to a Lifshitz transition of heavy-fermion bands. In the second part of the thesis, we study various aspects of magnetic pi fluxes in the Kane-Mele-Hubbard model of a correlated topological insulator. We describe a numerical measurement of the topological index, based on the localized mid-gap states that are provided by pi flux insertions. Furthermore, we take advantage of the intrinsic spin degree of freedom of a pi flux to devise instances of interacting quantum spin systems. In the third part of the thesis, we introduce and characterize the Kane-Mele-Hubbard model on the pi flux honeycomb lattice. We place particular emphasis on the correlations effects along the one-dimensional boundary of the lattice and compare results from a bosonization study with finite-size quantum Monte Carlo simulations.},
  subject      = {Schwere-Fermionen-System},
  language  = {en}
}
@phdthesis{Werner2014,
  author    = {Werner, Jan},
  title     = {Numerical Simulations of Heavy Fermion Systems: From He-3 Bilayers to Topological Kondo Insulators},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-112039},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2014},
  abstract  = {Even though heavy fermion systems have been studied for a long time, a strong interest in heavy fermions persists to this day. While the basic principles of local moment formation, Kondo effect and formation of composite quasiparticles leading to a Fermi liquid, are under- stood, there remain many interesting open questions. A number of issues arise due to the interplay of heavy fermion physics with other phenomena like magnetism and superconduc- tivity. In this regard, experimental and theoretical investigations of He-3 can provide valuable insights. He-3 represents a unique realization of a quantum liquid. The fermionic nature of He-3 atoms, in conjunction with the absence of long-range Coulomb repulsion, makes this material an ideal model system to study Fermi liquid behavior. Bulk He-3 has been investigated for quite some time. More recently, it became possible to prepare and study layered He-3 systems, in particular single layers and bilayers. The pos- sibility of tuning various physical properties of the system by changing the density of He-3 and using different substrate materials makes layers of He-3 an ideal quantum simulator for investigating two-dimensional Fermi liquid phenomenology. In particular, bilayers of He-3 have recently been found to exhibit heavy fermion behavior. As a function of temperature, a crossover from an incoherent state with decoupled layers to a coherent Fermi liquid of composite quasiparticles was observed. This behavior has its roots in the hybridization of the two layers. The first is almost completely filled and subject to strong correlation effects, while the second layer is only partially filled and weakly correlated. The quasiparticles are formed due to the Kondo screening of localized moments in the first layer by the second-layer delocalized fermions, which takes place at a characteristic temperature scale, the coherence scale Tcoh. Tcoh can be tuned by changing the He-3 density. In particular, at a certain critical filling, the coherence scale is expected to vanish, corresponding to a divergence of the quasiparticle effective mass, and a breakdown of the Kondo effect at a quantum critical point. Beyond the critical point, the layers are decoupled. The first layer is a local moment magnet, while the second layer is an itinerant overlayer. However, already at a filling smaller than the critical value, preempting the critical point, the onset of a finite sample magnetization was observed. The character of this intervening phase remained unclear. Motivated by these experimental observations, in this thesis the results of model calcula- tions based on an extended Periodic Anderson Model are presented. The three particle ring exchange, which is the dominant magnetic exchange process in layered He-3, is included in the model. It leads to an effective ferromagnetic interaction between spins on neighboring sites. In addition, the model incorporates the constraint of no double occupancy by taking the limit of large local Coulomb repulsion. By means of Cellular DMFT, the model is investigated for a range of values of the chemical potential µ and inverse temperature β = 1/T . The method is a cluster extension to the Dy- namical Mean-Field Theory (DMFT), and allows to systematically include non-local correla- tions beyond the DMFT. The auxiliary cluster model is solved by a hybridization expansion CTQMC cluster solver, which provides unbiased, numerically exact results for the Green's function and other observables of interest. As a first step, the onset of Fermi liquid coherence is studied. At low enough temperature, the self-energy is found to exhibit a linear dependence on Matsubara frequency. Meanwhile, the spin susceptibility crossed over from a Curie-Weiss law to a Pauli law. Both observations serve as fingerprints of the Fermi liquid state. The heavy fermion state appears at a characteristic coherence scale Tcoh. This scale depends strongly on the density. While it is rather high for small filling, for larger filling Tcoh is increas- ingly suppressed. This involves a decreasing quasiparticle residue Z ∼ Tcoh and an enhanced mass renormalization m∗/m ∼ Tcoh-1. Extrapolation leads to a critical filling, where the co- herence scale is expected to vanish at a quantum critical point. At the same time, the effective mass diverges. This corresponds to a breakdown of the Kondo effect, which is responsible for the formation of quasiparticles, due to a vanishing of the effective hybridization between the layers. Taking only single-site DMFT results into account, the above scenario seems plausible. However, paramagnetic DMFT neglects the ring exchange interaction completely. In or- der to improve on this, Cellular DMFT simulations are conducted for small clusters of size Nc = 2 and 3. The results paint a different physical picture. The ring exchange, by favor- ing a ferromagnetic alignment of spins, competes with the Kondo screening. As a result, strong short-range ferromagnetic fluctuations appear at larger values of µ. By lowering the temperature, these fluctuations are enhanced at first. However, for T < Tcoh they are increas- ingly suppressed, which is consistent with Fermi liquid coherence. However, beyond a certain threshold value of µ, fluctuations persist to the lowest temperatures. At the same time, while not apparent in the DMFT results, the total occupation n increases quite strongly in a very narrow range around the same value of µ. The evolution of n with µ is always continuous, but hints at a discontinuity in the limit Nc → ∞. This first-order transition breaks the Kondo effect. Beyond the transition, a ferromagnetic state in the first layer is established, and the second layer becomes a decoupled overlayer. These observations provide a quite appealing interpretation of the experimental results. As a function of chemical potential, the Kondo breakdown quantum critical point is preempted by a first-order transition, where the layers decouple and the first layer turns into a ferromagnet. In the experimental situation, where the filling can be tuned directly, the discontinuous transition is mirrored by a phase separation, which interpolates between the Fermi liquid ground state at lower filling and the magnetic state at higher filling. This is precisely the range of the intervening phase found in the experiments, which is characterized by an onset of a finite sample magnetization. Besides the interplay of heavy fermion physics and magnetic exchange, recently the spin- orbit coupling, which is present in many heavy fermion materials, attracted a lot of interest. In the presence of time-reversal symmetry, due to spin-orbit coupling, there is the possibility of a topological ground state. It was recently conjectured that the energy scale of spin-orbit coupling can become dom- inant in heavy fermion materials, since the coherence scale and quasiparticle bandwidth are rather small. This can lead to a heavy fermion ground state with a nontrivial band topology; that is, a topological Kondo insulator (TKI). While being subject to strong correlation effects, this state must be adiabatically connected to a non-interacting, topological state. The idea of the topological ground state realized in prototypical Kondo insulators, in par- ticular SmB6, promises to shed light on some of the peculiarities of these materials, like a residual conductivity at the lowest temperatures, which have remained unresolved so far. In this work, a simple two-band model for two-dimensional topological Kondo insulators is devised, which is based on a single Kramer's doublet coupled to a single conduction band. The model is investigated in the presence of a Hubbard interaction as a function of interaction strength U and inverse temperature β. The bulk properties of the model are obtained by DMFT, with a hybridization expansion CTQMC impurity solver. The DMFT approximation of a local self-energy leads to a very simple way of computing the topological invariant. The results show that with increasing U the system can be driven through a topological phase transition. Interestingly, the transition is between distinct topological insulating states, namely the Γ-phase and M-phase. This appearance of different topological phases is possible due to the symmetry of the underlying square lattice. By adiabatically connecting both in- teracting states with the respective non-interacting state, it is shown that the transition indeed drives the system from the Γ-phase to the M-phase. A different behavior can be observed by pushing the bare position of the Kramer's doublet to higher binding energies. In this case, the non-interacting starting point has a trivial band topology. By switching on the interaction, the system can be tuned through a quantum phase transition, with a closing of the band gap. Upon reopening of the band gap, the system is in the Γ-phase, i. e. a topological insulator. By increasing the interaction strength further, the system moves into a strongly correlated regime. In fact, close to the expected transition to the M phase, the mass renormalization becomes quite substantial. While absent in the para- magnetic DMFT simulations conducted, it is conceivable that instead of a topological phase transition, the system undergoes a time-reversal symmetry breaking, magnetic transition. The regime of strong correlations is studied in more detail as a function of temperature, both in the bulk and with open boundary conditions. A quantity which proved very useful is the bulk topological invariant Ns, which can be generalized to finite interaction strength and temperature. In particular, it can be used to define a temperature scale T ∗ for the onset of the topological state. Rescaling the results for Ns, a nice data collapse of the results for different values of U, from the local moment regime to strongly mixed valence, is obtained. This hints at T ∗ being a universal low energy scale in topological Kondo insulators. Indeed, by comparing T ∗ with the coherence scale extracted from the self-energy mass renormalization, it is found that both scales are equivalent up to a constant prefactor. Hence, the scale T ∗ obtained from the temperature dependence of topological properties, can be used as an independent measure for Fermi liquid coherence. This is particularly useful in the experimentally relevant mixed valence regime, where charge fluctuations cannot be neglected. Here, a separation of the energy scales related to spin and charge fluctuations is not possible. The importance of charge fluctuations becomes evident in the extent of spectral weight transfer as the temperature is lowered. For mixed valence, while the hybridization gap emerges, a substantial amount of spectral weight is shifted from the vicinity of the Fermi level to the lower Hubbard band. In contrast, this effect is strongly suppressed in the local moment regime. In addition to the bulk properties, the spectral function for open boundaries is studied as a function of temperature, both in the local moment and mixed valence regime. This allows an investigation of the emergence of topological edge states with temperature. The method used here is the site-dependent DMFT, which is a generalization of the conventional DMFT to inhomogeneous systems. The hybridization expansion CTQMC algorithm is used as impurity solver. By comparison with the bulk results for the topological quantity Ns, it is found that the temperature scale for the appearance of the topological edge states is T ∗, both in the mixed valence and local moment regime.},
  subject      = {Fermionensystem},
  language  = {en}
}
@phdthesis{Bruene2014,
  author    = {Br{\"u}ne, Christoph},
  title     = {HgTe based topological insulators},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-105127},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2014},
  abstract  = {Recently a new state of matter was discovered in which the bulk insulating state in a material is accompanied by conducting surface or edge states. This new state of matter can be distinguished from a conventional insulator phase by the topological properties of its band structure which led to the name "topological insulators". Experimentally, topological insulator states are mostly found in systems characterized by a band inversion compared to conventional systems. In most topological insulator systems, this is caused by a combination of energetically close bands and spin orbit coupling. Such properties are found in systems with heavy elements like Hg and Bi. And indeed, the first experimental discovery of a topological insulator succeeded in HgTe quantum wells and later also in BiSb bulk systems. Topological insulators are of large interest due to their unique properties: In 2-dimensional topological insulators one dimensional edge states form without the need of an external magnetic field (in contrast to the quantum Hall effect). These edge states feature a linear band dispersion, a so called Dirac dispersion. The quantum spin Hall states are helical edge states, which means they consist of counterpropagating oppositely spin polarized edge channels. They are therefore of great potential for spintronic applications as well as building blocks for new more exotic states like Majorana Fermions. 3-dimensional topological insulators feature 2-dimensional surface states with only one Dirac band (also called Dirac cone) on each surface and an interesting spin texture where spin and momentum are locked perpendicular to each other in the surface plane. This unique surface band structure is predicted to be able to host several exotic states like e.g. Majorana Fermions (in combination with superconductors) and magnetic monopole like excitations. This PhD thesis will summarize the discovery of topological insulators and highlights the developments on their experimental observations. The work focuses on HgTe which is up to now the only topological insulator material where the expected properties are unambiguously demonstrated in transport experiments. In HgTe, the topological insulator properties arise from the inversion of the Gamma_6 and Gamma_8 bands. The band inversion in HgTe is due to a combination of a high spin orbit splitting in Te and large energy corrections (due to the mass-velocity term) to the energy levels in Hg. Bulk HgTe, however, is a semimetal, which means for the conversion into a topological insulator a band gap has to be opened. In two dimensions (HgTe quantum well structures) this is achieved via quantum confinement, which opens a band gap between the quantum well subbands. In three dimensions, strain is used to lift the degeneracy of the semimetallic Gamma_8 bands opening up a band gap. The thesis is structured as follows: - The first chapter of this thesis will give a brief overview on discoveries in the field of topological insulators. It focuses on works relevant to experimental results presented in the following chapters. This includes a short outline of the early predictions and a summary of important results concerning 2-dimensional topological insulators while the final section discusses observations concerning 3-dimensional topological insulators. - The discovery of the quantum spin Hall effect in HgTe marked the first experimental observation of a topological insulator. Chapter 2 will focus on HgTe quantum wells and the quantum spin Hall effect. Above a critical thickness, HgTe quantum wells are predicted to host the quantum spin Hall state, the signature of a 2-dimensional topological insulator. HgTe quantum wells exhibiting low carrier concentrations and at the same time high carrier mobilities are required to be able to measure the quantum spin Hall effect. The growth of such high quality HgTe quantum wells was one of the major goals for this work. Continuous optimization of the substrate preparation and growth conditions resulted in controlled carrier densities down to a few 10^10 cm^-2. At the same time, carrier mobilities exceeding 1 x 10^6 cm^2/Vs have been achieved, which provides mean free paths of several micrometers in the material. Thus the first experimental evidence for the existence of the quantum spin Hall edge states succeeded in transport experiments on microstructures: When the Fermi energy was located in the bulk band gap a residual quantized resistance of 2e^2/h was found. Further experiments focused on investigating the nature of transport in this regime. By non-local measurements the edge state character could be established. The measured non-local resistances corresponded well with predictions from the Landauer-B{\"u}ttiker theory applied to transport in helical edge channels. In a final set of experiments the spin polarization of the edge channels was investigated. Here, we could make use of the advantage that HgTe quantum well structures exhibit a large Rashba spin orbit splitting. In systems with a large Rashba spin orbit splitting a spin accumulation is expected to occur at the edge of the sample perpendicular to a current flow. This so-called spin Hall effect was then used as a spin injector and detector. Using split gate devices it was possible to bring spin Hall and quantum spin Hall state into direct contact, which enabled an all electrical detection of the spin polarization of the quantum spin Hall edge channels. - HgTe as a 3-dimensional topological insulator will be presented in chapter 3. Straining the HgTe layer enables the observation of topological insulator behavior. It was found that strain can be easily implemented during growth by using CdTe substrates. CdTe has a slightly larger lattice constant than HgTe and therefore leads to tensile strain in the HgTe layer as long as the growth is pseudomorphic. Magnetotransport studies showed the emergence of quantum Hall transport with characteristic signatures of a Dirac type bandstructure. Thus, this result marks the first observation of the quantum Hall effect in the surface states of a 3-dimensional topological insulator. Transport experiments on samples fitted with a top gate enabled the identification of contributions from individual surfaces. Furthermore, the surface state quantum Hall effect was found to be surprisingly stable, perturbations due to additional bulk transport could not be found, even at high carrier densities of the system. - Chapters 4 - 6 serve as in depth overviews of selected works: Chapter 4 presents a detailed overview on the all electrical detection of the spin Hall effect in HgTe quantum wells. The detection of the spin polarization of the quantum spin Hall effect is shown in chapter 5 and chapter 6 gives a detailed overview on the quantum Hall effect originating from the topological surface state in strained bulk HgTe. The investigations discussed in this thesis pioneered the experimental work on the transport properties of topological insulator systems. The understanding of the fundamental properties of topological insulators enables new experiments in which e.g. the inclusion of magnetic dopants or the interplay between topological insulator and superconductors can be investigated in detail.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Budich2012,
  author    = {Budich, Jan Carl},
  title     = {Fingerprints of Geometry and Topology on Low Dimensional Mesoscopic Systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-76847},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {In this PhD thesis, the fingerprints of geometry and topology on low dimensional mesoscopic systems are investigated. In particular, holographic non-equilibrium transport properties of the quantum spin Hall phase, a two dimensional time reversal symmetric bulk insulating phase featuring one dimensional gapless helical edge modes are studied. In these metallic helical edge states, the spin and the direction of motion of the charge carriers are locked to each other and counter-propagating states at the same energy are conjugated by time reversal symmetry. This phenomenology entails a so called topological protection against elastic single particle backscattering by time reversal symmetry. We investigate the limitations of this topological protection by studying the influence of inelastic processes as induced by the interplay of phonons and extrinsic spin orbit interaction and by taking into account multi electron processes due to electron-electron interaction, respectively. Furthermore, we propose possible spintronics applications that rely on a spin charge duality that is uniquely associated with the quantum spin Hall phase. This duality is present in the composite system of two helical edge states with opposite helicity as realized on the two opposite edges of a quantum spin Hall sample with ribbon geometry. More conceptually speaking, the quantum spin Hall phase is the first experimentally realized example of a symmetry protected topological state of matter, a non-interacting insulating band structure which preserves an anti-unitary symmetry and is topologically distinct from a trivial insulator in the same symmetry class with totally localized and hence independent atomic orbitals. In the first part of this thesis, the reader is provided with a fairly self-contained introduction into the theoretical concepts underlying the timely research field of topological states of matter. In this context, the topological invariants characterizing these novel states are viewed as global analogues of the geometric phase associated with a cyclic adiabatic evolution. Whereas the detailed discussion of the topological invariants is necessary to gain deeper insight into the nature of the quantum spin Hall effect and related physical phenomena, the non-Abelian version of the local geometric phase is employed in a proposal for holonomic quantum computing with spin qubits in quantum dots.},
  subject      = {Topologischer Isolator},
  language  = {en}
}