@article{UenzelmannBentmannFiggemeieretal.2021, author = {{\"U}nzelmann, M. and Bentmann, H. and Figgemeier, T. and Eck, P. and Neu, J. N. and Geldiyev, B. and Diekmann, F. and Rohlf, S. and Buck, J. and Hoesch, M. and Kall{\"a}ne, M. and Rossnagel, K. and Thomale, R. and Siegrist, T. and Sangiovanni, G. and Di Sante, D. and Reinert, F.}, title = {Momentum-space signatures of Berry flux monopoles in the Weyl semimetal TaAs}, series = {Nature Communications}, volume = {12}, journal = {Nature Communications}, number = {1}, doi = {10.1038/s41467-021-23727-3}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-260719}, year = {2021}, abstract = {Since the early days of Dirac flux quantization, magnetic monopoles have been sought after as a potential corollary of quantized electric charge. As opposed to magnetic monopoles embedded into the theory of electromagnetism, Weyl semimetals (WSM) exhibit Berry flux monopoles in reciprocal parameter space. As a function of crystal momentum, such monopoles locate at the crossing point of spin-polarized bands forming the Weyl cone. Here, we report momentum-resolved spectroscopic signatures of Berry flux monopoles in TaAs as a paradigmatic WSM. We carried out angle-resolved photoelectron spectroscopy at bulk-sensitive soft X-ray energies (SX-ARPES) combined with photoelectron spin detection and circular dichroism. The experiments reveal large spin- and orbital-angular-momentum (SAM and OAM) polarizations of the Weyl-fermion states, resulting from the broken crystalline inversion symmetry in TaAs. Supported by first-principles calculations, our measurements image signatures of a topologically non-trivial winding of the OAM at the Weyl nodes and unveil a chirality-dependent SAM of the Weyl bands. Our results provide directly bulk-sensitive spectroscopic support for the non-trivial band topology in the WSM TaAs, promising to have profound implications for the study of quantum-geometric effects in solids. Weyl semimetals exhibit Berry flux monopoles in momentum-space, but direct experimental evidence has remained elusive. Here, the authors reveal topologically non-trivial winding of the orbital-angular-momentum at the Weyl nodes and a chirality-dependent spin-angular-momentum of the Weyl bands, as a direct signature of the Berry flux monopoles in TaAs.}, 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} } @article{WagnerCrippaAmariccietal.2023, author = {Wagner, N. and Crippa, L. and Amaricci, A. and Hansmann, P. and Klett, M. and K{\"o}nig, E. J. and Sch{\"a}fer, T. and Di Sante, D. and Cano, J. and Millis, A. J. and Georges, A. and Sangiovanni, G.}, title = {Mott insulators with boundary zeros}, series = {Nature Communications}, volume = {14}, journal = {Nature Communications}, doi = {10.1038/s41467-023-42773-7}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-358150}, year = {2023}, abstract = {The topological classification of electronic band structures is based on symmetry properties of Bloch eigenstates of single-particle Hamiltonians. In parallel, topological field theory has opened the doors to the formulation and characterization of non-trivial phases of matter driven by strong electron-electron interaction. Even though important examples of topological Mott insulators have been constructed, the relevance of the underlying non-interacting band topology to the physics of the Mott phase has remained unexplored. Here, we show that the momentum structure of the Green's function zeros defining the "Luttinger surface" provides a topological characterization of the Mott phase related, in the simplest description, to the one of the single-particle electronic dispersion. Considerations on the zeros lead to the prediction of new phenomena: a topological Mott insulator with an inverted gap for the bulk zeros must possess gapless zeros at the boundary, which behave as a form of "topological antimatter" annihilating conventional edge states. Placing band and Mott topological insulators in contact produces distinctive observable signatures at the interface, revealing the otherwise spectroscopically elusive Green's function zeros.}, language = {en} } @article{VigliottiCalzonaTraversoZianietal.2023, author = {Vigliotti, Lucia and Calzona, Alessio and Traverso Ziani, Niccol{\`o} and Bergeret, F. Sebastian and Sassetti, Maura and Trauzettel, Bj{\"o}rn}, title = {Effects of the spatial extension of the edge channels on the interference pattern of a helical Josephson junction}, series = {Nanomaterials}, volume = {13}, journal = {Nanomaterials}, number = {3}, issn = {2079-4991}, doi = {10.3390/nano13030569}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-304846}, year = {2023}, abstract = {Josephson junctions (JJs) in the presence of a magnetic field exhibit qualitatively different interference patterns depending on the spatial distribution of the supercurrent through the junction. In JJs based on two-dimensional topological insulators (2DTIs), the electrons/holes forming a Cooper pair (CP) can either propagate along the same edge or be split into the two edges. The former leads to a SQUID-like interference pattern, with the superconducting flux quantum ϕ\(_0\) (where ϕ\(_0\)=h/2e) as a fundamental period. If CPs' splitting is additionally included, the resultant periodicity doubles. Since the edge states are typically considered to be strongly localized, the critical current does not decay as a function of the magnetic field. The present paper goes beyond this approach and inspects a topological JJ in the tunneling regime featuring extended edge states. It is here considered the possibility that the two electrons of a CP propagate and explore the junction independently over length scales comparable to the superconducting coherence length. As a consequence of the spatial extension, a decaying pattern with different possible periods is obtained. In particular, it is shown that, if crossed Andreev reflections (CARs) are dominant and the edge states overlap, the resulting interference pattern features oscillations whose periodicity approaches 2ϕ\(_0\).}, 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} } @article{StuehlerKowalewskiReisetal.2022, author = {St{\"u}hler, R. and Kowalewski, A. and Reis, F. and Jungblut, D. and Dominguez, F. and Scharf, B. and Li, G. and Sch{\"a}fer, J. and Hankiewicz, E. M. and Claessen, R.}, title = {Effective lifting of the topological protection of quantum spin Hall edge states by edge coupling}, series = {Nature Communications}, volume = {13}, journal = {Nature Communications}, doi = {10.1038/s41467-022-30996-z}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-300886}, year = {2022}, abstract = {The scientific interest in two-dimensional topological insulators (2D TIs) is currently shifting from a more fundamental perspective to the exploration and design of novel functionalities. Key concepts for the use of 2D TIs in spintronics are based on the topological protection and spin-momentum locking of their helical edge states. In this study we present experimental evidence that topological protection can be (partially) lifted by pairwise coupling of 2D TI edges in close proximity. Using direct wave function mapping via scanning tunneling microscopy/spectroscopy (STM/STS) we compare isolated and coupled topological edges in the 2D TI bismuthene. The latter situation is realized by natural lattice line defects and reveals distinct quasi-particle interference (QPI) patterns, identified as electronic Fabry-P{\´e}rot resonator modes. In contrast, free edges show no sign of any single-particle backscattering. These results pave the way for novel device concepts based on active control of topological protection through inter-edge hybridization for, e.g., electronic Fabry-P{\´e}rot interferometry.}, language = {en} } @article{SessiBiswasBathonetal.2016, author = {Sessi, Paolo and Biswas, Rudro R. and Bathon, Thomas and Storz, Oliver and Wilfert, Stefan and Barla, Alessandro and Kokh, Konstantin A. and Tereshchenko, Oleg E. and Fauth, Kai and Bode, Matthias and Balatsky, Alexander V.}, title = {Dual nature of magnetic dopants and competing trends in topological insulators}, series = {Nature Communications}, volume = {7}, journal = {Nature Communications}, doi = {10.1038/ncomms12027}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-172704}, year = {2016}, abstract = {Topological insulators interacting with magnetic impurities have been reported to host several unconventional effects. These phenomena are described within the framework of gapping Dirac quasiparticles due to broken time-reversal symmetry. However, the overwhelming majority of studies demonstrate the presence of a finite density of states near the Dirac point even once topological insulators become magnetic. Here, we map the response of topological states to magnetic impurities at the atomic scale. We demonstrate that magnetic order and gapless states can coexist. We show how this is the result of the delicate balance between two opposite trends, that is, gap opening and emergence of a Dirac node impurity band, both induced by the magnetic dopants. Our results evidence a more intricate and rich scenario with respect to the once generally assumed, showing how different electronic and magnetic states may be generated and controlled in this fascinating class of materials.}, 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{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} } @article{OostingaMaierSchueffelgenetal.2013, author = {Oostinga, Jeroen B. and Maier, Luis and Sch{\"u}ffelgen, Peter and Knott, Daniel and Ames, Christopher and Br{\"u}ne, Christoph and Tkachov, Grigory and Buhmann, Hartmut and Molenkamp, Laurens W.}, title = {Josephson Supercurrent through the Topological Surface States of Strained Bulk HgTe}, series = {Physical Review X}, volume = {3}, journal = {Physical Review X}, number = {021007}, doi = {10.1103/PhysRevX.3.021007}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-129834}, year = {2013}, abstract = {Strained bulk HgTe is a three-dimensional topological insulator, whose surface electrons have a high mobility (~ 30 000 cm\(^2\)=Vs), while its bulk is effectively free of mobile charge carriers. These properties enable a study of transport through its unconventional surface states without being hindered by a parallel bulk conductance. Here, we show transport experiments on HgTe-based Josephson junctions to investigate the appearance of the predicted Majorana states at the interface between a topological insulator and a superconductor. Interestingly, we observe a dissipationless supercurrent flow through the topological surface states of HgTe. The current-voltage characteristics are hysteretic at temperatures below 1 K, with critical supercurrents of several microamperes. Moreover, we observe a magnetic-field-induced Fraunhofer pattern of the critical supercurrent, indicating a dominant \(2\pi\)-periodic Josephson effect in the unconventional surface states. Our results show that strained bulk HgTe is a promising material system to get a better understanding of the Josephson effect in topological surface states, and to search for the manifestation of zero-energy Majorana states in transport experiments.}, language = {en} } @article{MaCalvoWangetal.2015, author = {Ma, Eric Yue and Calvo, M. Reyes and Wang, Jing and Lian, Biao and M{\"u}hlbauer, Mathias and Br{\"u}ne, Christoph and Cui, Yong-Tao and Lai, Keji and Kundhikanjana, Worasom and Yang, Yongliang and Baenninger, Matthias and K{\"o}nig, Markus and Ames, Christopher and Buhmann, Hartmut and Leubner, Philipp and Molenkamp, Laurens W. and Zhang, Shou-Cheng and Goldhaber-Gordon, David and Kelly, Michael A. and Shen, Zhi-Xun}, title = {Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry}, series = {Nature Communications}, volume = {6}, journal = {Nature Communications}, number = {7252}, doi = {10.1038/ncomms8252}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-143185}, year = {2015}, abstract = {The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a noninverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. This indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.}, language = {en} } @article{KoenigBaenningerGarciaetal.2013, author = {K{\"o}nig, Markus and Baenninger, Matthias and Garcia, Andrei G. F. and Harjee, Nahid and Pruitt, Beth L. and Ames, C. and Leubner, Philipp and Br{\"u}ne, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W. and Goldhaber-Gordon, David}, title = {Spatially Resolved Study of Backscattering in the Quantum Spin Hall State}, series = {Physical Review X}, volume = {3}, journal = {Physical Review X}, number = {2}, issn = {2160-3308}, doi = {10.1103/PhysRevX.3.021003}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-127225}, pages = {21003}, year = {2013}, abstract = {The discovery of the quantum spin Hall (QSH) state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the quantum spin Hall state have confirmed the presence of edge states, showed ballistic edge transport in micron-sized samples, and demonstrated the spin polarization of the helical edge states. While these experiments have confirmed the broad theoretical model, the properties of the QSH edge states have not yet been investigated on a local scale. Using scanning gate microscopy to perturb the QSH edge states on a submicron scale, we identify well-localized scattering sites which likely limit the expected nondissipative transport in the helical edge channels. In the micron-sized regions between the scattering sites, the edge states appear to propagate unperturbed, as expected for an ideal QSH system, and are found to be robust against weak induced potential fluctuations.}, language = {en} } @article{KernreiterGovernaleZuelickeetal.2016, author = {Kernreiter, T. and Governale, M. and Z{\"u}licke, U. and Hankiewicz, E. M.}, title = {Anomalous Spin Response and Virtual-Carrier-Mediated Magnetism in a Topological Insulator}, series = {Physical Review X}, volume = {6}, journal = {Physical Review X}, number = {021010}, doi = {10.1103/PhysRevX.6.021010}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-166582}, year = {2016}, abstract = {We present a comprehensive theoretical study of the static spin response in HgTe quantum wells, revealing distinctive behavior for the topologically nontrivial inverted structure. Most strikingly, the q=0 (long-wavelength) spin susceptibility of the undoped topological-insulator system is constant and equal to the value found for the gapless Dirac-like structure, whereas the same quantity shows the typical decrease with increasing band gap in the normal-insulator regime. We discuss ramifications for the ordering of localized magnetic moments present in the quantum well, both in the insulating and electron-doped situations. The spin response of edge states is also considered, and we extract effective Land{\´e} g factors for the bulk and edge electrons. The variety of counterintuitive spin-response properties revealed in our study arises from the system's versatility in accessing situations where the charge-carrier dynamics can be governed by ordinary Schr{\"o}dinger-type physics; it mimics the behavior of chiral Dirac fermions or reflects the material's symmetry-protected topological order.}, language = {en} } @article{FleszarHanke2015, author = {Fleszar, Andrzej and Hanke, Werner}, title = {Two-dimensional metallicity with a large spin-orbit splitting: DFT calculations of the atomic, electronic, and spin structures of the Au/Ge(111)-(√3 x √3)R30° surface}, series = {Advances in Condensed Matter Physics}, volume = {2015}, journal = {Advances in Condensed Matter Physics}, number = {531498}, doi = {10.1155/2015/531498}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-149221}, year = {2015}, abstract = {Density functional theory (DFT) is applied to study the atomic, electronic, and spin structures of the Au monolayer at the Ge(111) surface. It is found that the theoretically determined most stable atomic geometry is described by the conjugated honeycomb-chained-trimer (CHCT) model, in a very good agreement with experimental data. The calculated electronic structure of the system, being in qualitatively good agreement with the photoemission measurements, shows fingerprints of the many-body effects (self-interaction corrections) beyond the LDA or GGA approximations. The most interesting property of this surface system is the large spin splitting of its metallic surface bands and the undulating spin texture along the hexagonal Fermi contours, which highly resembles the spin texture at the Dirac state of the topological insulator Bi\(_{2}\)Te\(_{3}\). These properties make this system particularly interesting from both fundamental and technological points of view.}, language = {en} } @article{DziomShuvaevPimenovetal.2017, author = {Dziom, V. and Shuvaev, A. and Pimenov, A. and Astakhov, G.V. and Ames, C. and Bendias, K. and B{\"o}ttcher, J. and Tkachov, G. and Hankiewicz, E.M. and Br{\"u}ne, C. and Buhmann, H. and Molenkamp, L.W.}, title = {Observation of the universal magnetoelectric effect in a 3D topological insulator}, series = {Nature Communications}, volume = {8}, journal = {Nature Communications}, number = {15197}, doi = {10.1038/ncomms15197}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-170875}, year = {2017}, abstract = {The electrodynamics of topological insulators (TIs) is described by modified Maxwell's equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e\(^{2}\)/2E\(_{0}\)hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.}, language = {en} } @article{BrueneThienelStuiberetal.2014, author = {Br{\"u}ne, Christoph and Thienel, Cornelius and Stuiber, Michael and B{\"o}ttcher, Jan and Buhmann, Hartmut and Novik, Elena G. and Liu, Chao-Xing and Hankiewicz, Ewelina M. and Molenkamp, Laurens W.}, title = {Dirac-Screening Stabilized Surface-State Transport in a Topological Insulator}, series = {Physical Review X}, volume = {4}, journal = {Physical Review X}, number = {4}, issn = {2160-3308}, doi = {10.1103/PhysRevX.4.041045}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-118091}, pages = {041045}, year = {2014}, abstract = {We report magnetotransport studies on a gated strained HgTe device. This material is a three-dimensional topological insulator and exclusively shows surface-state transport. Remarkably, the Landau-level dispersion and the accuracy of the Hall quantization remain unchanged over a wide density range (3×1011  cm-2