@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{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{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{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{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{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{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{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{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{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}
}