@phdthesis{Maier2018,
  author    = {Maier, Patrick},
  title     = {Memristanz und Memkapazit{\"a}t von Quantenpunkt-Speichertransistoren: Realisierung neuromorpher und arithmetischer Operationen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-164234},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2018},
  abstract  = {In dieser Arbeit werden Quantenpunkt-Speichertransistoren basierend auf modulationsdotierten GaAs/AlGaAs Heterostrukturen mit vorpositionierten InAs Quantenpunkten vorgestellt, welche in Abh{\"a}ngigkeit der Ladung auf den Quantenpunkten unterschiedliche Widerst{\"a}nde und Kapazit{\"a}ten aufweisen. Diese Ladungsabh{\"a}ngigkeiten f{\"u}hren beim Anlegen von periodischen Spannungen zu charakteristischen, durch den Ursprung gehenden Hysteresen in der Strom-Spannungs- und der Ladungs-Spannungs-Kennlinie. Die ladungsabh{\"a}ngigen Widerst{\"a}nde und Kapazit{\"a}ten erm{\"o}glichen die Realisierung von neuromorphen Operationen durch Nachahmung von synaptischen Funktionalit{\"a}ten und arithmetischen Operationen durch Integration von Spannungs- und Lichtpulsen.},
  subject      = {Nichtfl{\"u}chtiger Speicher},
  language  = {de}
}
@phdthesis{Boettcher2021,
  author    = {B{\"o}ttcher, Jan Frederic},
  title     = {Fate of Topological States of Matter in the Presence of External Magnetic Fields},
  doi       = {10.25972/OPUS-22045},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-220451},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {The quantum Hall (QH) effect, which can be induced in a two-dimensional (2D) electron gas by an external magnetic field, paved the way for topological concepts in condensed matter physics. While the QH effect can for that reason not exist without Landau levels, there is a plethora of topological phases of matter that can exist even in the absence of a magnetic field. For instance, the quantum spin Hall (QSH), the quantum anomalous Hall (QAH), and the three-dimensional (3D) topological insulator (TI) phase are insulating phases of matter that owe their nontrivial topology to an inverted band structure. The latter results from a strong spin-orbit interaction or, generally, from strong relativistic corrections. The main objective of this thesis is to explore the fate of these preexisting topological states of matter, when they are subjected to an external magnetic field, and analyze their connection to quantum anomalies. In particular, the realization of the parity anomaly in solid state systems is discussed. Furthermore, band structure engineering, i.e., changing the quantum well thickness, the strain, and the material composition, is employed to manipulate and investigate various topological properties of the prototype TI HgTe. Like the QH phase, the QAH phase exhibits unidirectionally propagating metallic edge channels. But in contrast to the QH phase, it can exist without Landau levels. As such, the QAH phase is a condensed matter analog of the parity anomaly. We demonstrate that this connection facilitates a distinction between QH and QAH states in the presence of a magnetic field. We debunk therefore the widespread belief that these two topological phases of matter cannot be distinguished, since they are both described by a \$\mathbb{Z}\$ topological invariant. To be more precise, we demonstrate that the QAH topology remains encoded in a peculiar topological quantity, the spectral asymmetry, which quantifies the differences in the number of states between the conduction and valence band. Deriving the effective action of QAH insulators in magnetic fields, we show that the spectral asymmetry is thereby linked to a unique Chern-Simons term which contains the information about the QAH edge states. As a consequence, we reveal that counterpropagating QH and QAH edge states can emerge when a QAH insulator is subjected to an external magnetic field. These helical-like states exhibit exotic properties which make it possible to disentangle QH and QAH phases. Our findings are of particular importance for paramagnetic TIs in which an external magnetic field is required to induce the QAH phase. A byproduct of the band inversion is the formation of additional extrema in the valence band dispersion at large momenta (the `camelback'). We develop a numerical implementation of the \$8 \times 8\$ Kane model to investigate signatures of the camelback in (Hg,Mn)Te quantum wells. Varying the quantum well thickness, as well as the Mn-concentration, we show that the class of topologically nontrivial quantum wells can be subdivided into direct gap and indirect gap TIs. In direct gap TIs, we show that, in the bulk \$p\$-regime, pinning of the chemical potential to the camelback can cause an onset to QH plateaus at exceptionally low magnetic fields (tens of mT). In contrast, in indirect gap TIs, the camelback prevents the observation of QH plateaus in the bulk \$p\$-regime up to large magnetic fields (a few tesla). These findings allowed us to attribute recent experimental observations in (Hg,Mn)Te quantum wells to the camelback. Although our discussion focuses on (Hg,Mn)Te, our model should likewise apply to other topological materials which exhibit a camelback feature in their valence band dispersion. Furthermore, we employ the numerical implementation of the \$8\times 8\$ Kane model to explore the crossover from a 2D QSH to a 3D TI phase in strained HgTe quantum wells. The latter exhibit 2D topological surface states at their interfaces which, as we demonstrate, are very sensitive to the local symmetry of the crystal lattice and electrostatic gating. We determine the classical cyclotron frequency of surface electrons and compare our findings with experiments on strained HgTe.},
  subject      = {Topologie},
  language  = {en}
}
@phdthesis{Daumer2005,
  author    = {Daumer, Volker},
  title     = {Phase coherent transport phenomena in HgTe quantum well structures},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-15538},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {Although spintronics has aroused increasing interest, much fundamental research has to be done. One important issue is the control over the electronic spin. Therefore, spin and phase coherent transport are very important phenomena. This thesis describes experiments with mercury based quantum well structures. This narrow gap material provides a very good template to study spin related effects. It exhibits large Zeeman spin splitting and Rashba spin-orbit splitting. The latter is at least four to five times larger than in III-V semiconductors. Initially a short review on the transport theory was presented. The main focus as on quantisation effects that are important to understand the related experiments. Thus, Shubnikov-de Haas and the quantum Hall effect have been analysed. Due to the first fabrication of nanostructures on Hg-based quantum well samples, the observation of ballistic transport effects could be expected. Hence, the Landauer-B¨uttiker theory has been introduced which gives the theoretical background to understand such effects. With respect to the main topic of this thesis, phase coherence has been introduced in detail. Experiments, where coherence effects could be observed, have been explained theoretically. Here, possible measurement setups have been discussed, e.g., a ring shaped structure to investigate the Aharonov-Bohm and related effects. Due to the fact, that all experiments, described in this thesis, were performed on Hg-based samples, the exceptional position of such samples among the \&\#147;classical\&\#148; semiconductors has been clarified. Hg1-xMnx Te quantum wells are type-III QWs in contrast to the type-I QWs formed by e.g., GaAs/AlGaAs heterostructures. With a well width of more than 6 nm and a manganese content of less than 7\% they exhibit an inverted band alignment. Band structure calculations based on self consistent Hartree calculations have been presented. The common description of a diluted magnetic semiconductor with the Brillouin function has been introduced and the experiments to obtain the empiric parameters T0 and S0 have been presented. Rashba spin-orbit splitting and giant Zeeman splitting have been explained theoretically and the magnetic ordering of a spin glass as well as the relevant interactions therein have been discussed. The next chapter describes the first realisation of nanostructures on Hg-based heterostructures. Several material specific problems have been solved, but the unique features of this material system mentioned above justify the effort. Interesting new insight could be found and will be found with these structures. Onto a series of QW samples, cross-shaped structures with several lead widths have been patterned. With the non-local resistance measurement setup, evidence for quasiballistic transport was demonstrated in cross-shaped structures with lead widths down to 0.45 mm. The non-local bend resistance and a regime of rebound trajectories as well as the anomalous Hall effect could be identified. Monte-Carlo simulations of the classical electron trajectories have been performed. A good agreement with the experimental data has been achieved by taking a random scattering process into account. Encouraged by this success the technology has been improved and ring-shaped structures with radii down to 1 mm have been fabricated. Low temperature (below 100 mK), four terminal resistance measurements exhibit clear Aharonov-Bohm oscillations. The period of the oscillations agrees very well with a calculation that takes only the sample geometry into account. One goal using such a structure is the experimental prove of the spin-orbit Berry phase. Therefore an additional Shottky gate on top of the ring was needed. With this structure evidence for the Aharonov-Casher effect was observed. Here, a perpendicular applied electric field causes analogous oscillations as does the magnetic field in the AB effect. A subsequent change in the Rashba SO splitting due to several applied gate voltages while measuring the AB effect should reveal the SO Berry phase. Although initially evidence of a phase change was detected, a clear proof for the direct measurement of the SO Berry phase could not be found. In the future, with an advanced sample structure, e.g., with an additional Hall bar next to the ring, which permits a synchronous measurement of the Rashba splitting, it might be possible to measure the SO Berry phase directly. In manganese doped HgTe QWs two different effects simultaneously cause spin splitting: the giant Zeeman and the Rashba effect. By analysing the Shubnikovde Haas oscillations and the node positions of their beating pattern, it has been possible to separate these two effects. Whereas the Rashba effect can be identified by its dependence on the structure inversion asymmetry, varied by the applied gate voltage, the giant Zeeman splitting is extracted from its strong temperature dependence, because Rashba splitting is temperature independent. The analysis revealed, that the Rashba splitting is larger than or comparable to the giant Zeeman splitting even at moderately high magnetic fields. In an extraordinary HgMnTe QW sample, that exhibits the n= 1 quantum Hall plateau from less than 1 T up to 28 T, the anomalous Hall effect could be excluded. Intense studies on the temperature dependence of the QHE as well as band structure calculations have revealed this extraordinary behaviour to be an ordinary band structure effect of this system. In a series of mesoscopic structures on nonmagnetic and magnetic QWs, an investigation of the universal conductance uctuations have been carried out. In the},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{Koenig2007,
  author    = {K{\"o}nig, Markus},
  title     = {Spin-related transport phenomena in HgTe-based quantum well structures},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-27301},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {Within the scope of this thesis, spin related transport phenomena have been investigated in HgTe/HgCdTe quantum well structures. This material exhibits peculiar band structure properties, which result in a strong spin-orbit interaction of the Rashba type. An inverted band structure, i.e., a reversed ordering of the energy states in comparison to common semiconductors, is obtained for quantum well layers above a critical thickness. Furthermore, the band structure properties can be controlled in the experiments by moderate gate voltages. Most prominently, the type of carriers in HgTe quantum wells can be changed from n to p due to the narrow energy gap. Along with the inverted band structure, this unique transition is the basis for the demonstration of the Quantum Spin Hall state, which is characterized by the existence of two one-dimensional spin-polarized edge states propagating in opposite directions, while the Fermi level in the bulk is in the energy gap. Since elastic scattering is suppressed by time reversal symmetry, a quantized conductance for charge and spin transport is predicted. Our experiments provide the first experimental demonstration of the QSH state. For samples with characteristic dimensions below the inelastic mean free path, charge conductance close to the expected value of 2e^2/h has been observed. Strong indication for the edge state transport was found in the experiments as well. For large samples, potential fluctuations lead to the appearance of local n-conducting regions which are considered to be the dominant source of backscattering. When time reversal symmetry is broken in a magnetic field, elastic scattering becomes possible and conductance is significantly suppressed. The suppression relies on a dominant orbital effect in a perpendicular field and a smaller Zeeman-like effect present for any field direction. For large perpendicular fields, a re-entrant quantum Hall state appears. This unique property is directly related to the non-trivial QSH insulator state. While clear evidence for the properties of charge transport was provided, the spin properties could not be addressed. This might be the goal of future experiments. In another set of experiments, the intrinsic spin Hall effect was studied. Its investigation was motivated by the possibility to create and to detect pure spin currents and spin accumulation. A non-local charging attributed to the SHE has been observed in a p-type H-shaped structure with large SO interaction, providing the first purely electrical demonstration of the SHE in a semiconductor system. A possibly more direct way to study the spin Hall effects opens up when the spin properties of the QSH edge states are taken into account. Then, the QSH edge states can be used either as an injector or a detector of spin polarization, depending on the actual configuration of the device. The experimental results indicate the existence of both intrinsic SHE and the inverse SHE independently of each other. If a spin-polarized current is injected from the QSH states into a region with Rashba SO interaction, the precession of the spin can been observed via the SHE. Both the spin injection and precession might be used for the realization of a spin-FET similar to the one proposed by Datta and Das. Another approach for the realization of a spin-based FET relies on a spin-interference device, in which the transmission is controlled via the Aharonov-Casher phase and the Berry phase, both due to the SO interaction. In the presented experiments, ring structures with tuneable SO coupling were studied. A complex interference pattern is observed as a function of external magnetic field and gate voltage. The dependence on the Rashba splitting is attributed to the Aharonov-Casher phase, whereas effects due to the Berry phase remain unresolved. This interpretation is confirmed by theoretical calculations, where multi-channel transport through the device has been assumed in agreement with the experimental results. Thus, our experiments provide the first direct observation of the AC effect in semiconductor structures. In conclusion, HgTe quantum well structures have proven to be an excellent template for studying spin-related transport phenomena: The QSHE relies on the peculiar band structure of the material and the existence of both the SHE and the AC effect is a consequence of the substantial spin-orbit interaction. While convincing results have been obtained for the various effects, several questions can not be fully answered yet. Some of them may be addressed by more extensive studies on devices already available. Other issues, however, ask, e.g., for further advances in sample fabrication or new approaches by different measurements techniques. Thus, future experiments may provide new, compelling insights for both the effects discussed in this thesis and, more generally, other spin-orbit related transport properties.},
  subject      = {Spin-Bahn-Wechselwirkung},
  language  = {en}
}
@phdthesis{Lundt2020,
  author    = {Lundt, Felix Janosch Peter},
  title     = {Superconducting Hybrids at the Quantum Spin Hall Edge},
  doi       = {10.25972/OPUS-21642},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-216421},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {This Thesis explores hybrid structures on the basis of quantum spin Hall insulators, and in particular the interplay of their edge states and superconducting and magnetic order. Quantum spin Hall insulators are one example of topological condensed matter systems, where the topology of the bulk bands is the key for the understanding of their physical properties. A remarkable consequence is the appearance of states at the boundary of the system, a phenomenon coined bulk-boundary correspondence. In the case of the two-dimensional quantum spin Hall insulator, this is manifested by so-called helical edge states of counter-propagating electrons with opposite spins. They hold great promise, \emph{e.g.}, for applications in spintronics -- a paradigm for the transmission and manipulation of information based on spin instead of charge -- and as a basis for quantum computers. The beginning of the Thesis consists of an introduction to one-dimensional topological superconductors, which illustrates basic concepts and ideas. In particular, this includes the topological distinction of phases and the accompanying appearance of Majorana modes at their ends. Owing to their topological origin, Majorana modes potentially are essential building-blocks for topological quantum computation, since they can be exploited for protected operations on quantum bits. The helical edge states of quantum spin Hall insulators in conjunction with \$s\$-wave superconductivity and magnetism are a suitable candidate for the realization of a one-dimensional topological superconductor. Consequently, this Thesis investigates the conditions in which Majorana modes can appear. Typically, this happens between regions subjected to either only superconductivity, or to both superconductivity and magnetism. If more than one superconductor is present, the phase difference is of paramount importance, and can even be used to manipulate and move Majorana modes. Furthermore, the Thesis addresses the effects of the helical edge states on the anomalous correlation functions characterizing proximity-induced superconductivity. It is found that helicity and magnetism profoundly enrich their physical structure and lead to unconventional, exotic pairing amplitudes. Strikingly, the nonlocal correlation functions can be connected to the Majorana bound states within the system. Finally, a possible thermoelectric device on the basis of hybrid systems at the quantum spin Hall edge is discussed. It utilizes the peculiar properties of the proximity-induced superconductivity in order to create spin-polarized Cooper pairs from a temperature bias. Cooper pairs with finite net spin are the cornerstone of superconducting spintronics and offer tremendous potential for efficient information technologies.},
  subject      = {Mesoskopisches System},
  language  = {en}
}