@phdthesis{Wilfert2019,
  author    = {Wilfert, Stefan},
  title     = {Rastertunnelmikroskopische und -spektroskopische Untersuchung von Supraleitern und topologischen Supraleitern},
  doi       = {10.25972/OPUS-18059},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-180597},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {Quantencomputer k{\"o}nnen manche Probleme deutlich effizienter l{\"o}sen als klassische Rechner. Bisherige Umsetzungen leiden jedoch an einer zu geringen Dekoh{\"a}renzzeit, weshalb die Lebenszeit der Quantenzust{\"a}nde einen limitierenden Faktor darstellt. Topologisch gesch{\"u}tzte Anregungen, wie Majorana-Fermionen, k{\"o}nnten hingegen dieses Hindernis {\"u}berwinden. Diese lassen sich beispielsweise in topologischen Supraleitern realisieren. Bis zum jetzigen Zeitpunkt existieren nur wenige Materialien, die dieses Ph{\"a}nomen aufweisen. Daher ist das Verst{\"a}ndnis der elektronischen Eigenschaften f{\"u}r solche Verbindungen von großer Bedeutung. In dieser Dissertation wird die Koexistenz von Supraleitung an der Probenoberfl{\"a}che und topologischem Oberfl{\"a}chenzustand (engl. topological surface state, TSS) auf potentiellen topologischen Supraleitern {\"u}berpr{\"u}ft. Diese beiden Bedingungen sind essentiell zur Ausbildung von topologischer Supraleitung in zeitumkehrgesch{\"u}tzten Systemen. Hierzu wird mittels Landaulevelspektroskopie und Quasiteilcheninterferenz das Vorhandensein des TSS am Ferminiveau auf Tl\$_{x}\$Bi\$_{2}\$Te\$_{3}\$ und Nb\$_{x}\$Bi\$_{2}\$Se\$_{3}\$ verifiziert, die mittels Transportmessungen als supraleitend identifiziert wurden. Anschließend folgen hochaufgel{\"o}ste Spektroskopien an der Fermienergie, um die supraleitenden Eigenschaften zu analysieren. Zur Interpretation der analysierten Eigenschaften wird zu Beginn der Ni-haltige Schwere-Fermion-Supraleiter TlNi\$_{2}\$Se\$_{2}\$ untersucht, der eine vergleichbare {\"U}bergangstemperatur besitzt. Anhand diesem werden die g{\"a}ngigen Messmethoden der Rastertunnelmikroskopie und -spektroskopie f{\"u}r supraleitende Proben vorgestellt und die Leistungsf{\"a}higkeit der Messapparatur demonstriert. Im Einklang mit der Literatur zeigt sich ein \$s\$-Wellencharakter des Paarungsmechanismus sowie die Formation eines f{\"u}r Typ~II-Supraleiter typischen Abrikosov-Gitters in schwachen externen Magnetfeldern. Im folgenden Teil werden die potentiellen topologischen Supraleiter Tl\$_{x}\$Bi\$_{2}\$Te\$_{3}\$ und Nb\$_{x}\$Bi\$_{2}\$Se\$_{3}\$ begutachtet, f{\"u}r die eindeutig ein TSS best{\"a}tigt wird. Allerdings weisen beide Materialien keine Oberfl{\"a}chensupraleitung auf, was vermutlich durch eine Entkopplung der Oberfl{\"a}che vom Volumen durch Bandverbiegung zu erkl{\"a}ren ist. Unbeabsichtigte Kollisionen der Spitze mit der Probe f{\"u}hren jedoch zu supraleitenden Spitzen, die wesentlich erh{\"o}hte Werte f{\"u}r die kritische Temperatur und das kritische Feld zeigen. Der letzte Abschnitt widmet sich dem supraleitenden Substrat Nb(110), f{\"u}r den der Reinigungsprozess erl{\"a}utert wird. Hierbei sind kurze Heizschritte bis nahe des Schmelzpunktes n{\"o}tig, um die bei Umgebungsbedingungen entstehende Sauerstoffrekonstruktion effektiv zu entfernen. Des Weiteren werden die elektronischen Eigenschaften untersucht, die eine Oberfl{\"a}chenresonanz zum Vorschein bringen. Hochaufgel{\"o}ste Messungen lassen eine durch die BCS-Theorie gut repr{\"a}sentierte Struktur der supraleitenden Energiel{\"u}cke erkennen. Magnetfeldabh{\"a}ngige Experimente offenbaren zudem eine mit der Kristallstruktur vereinbare Anisotropie des Paarungspotentials. Mit diesen Erkenntnissen kann Nb(110) zuk{\"u}nftig als Ausgang f{\"u}r das Wachstum von topologischen Supraleitern herangezogen werden.},
  subject      = {Supraleitung},
  language  = {de}
}
@phdthesis{Wiedenmann2018,
  author    = {Wiedenmann, Jonas},
  title     = {Induced topological superconductivity in HgTe based nanostructures},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-162782},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2018},
  abstract  = {This thesis describes the studies of topological superconductivity, which is predicted to emerge when pair correlations are induced into the surface states of 2D and 3D topolog- ical insulators (TIs). In this regard, experiments have been designed to investigate the theoretical ideas first pioneered by Fu and Kane that in such system Majorana bound states occur at vortices or edges of the system [Phys. Rev. Lett. 100, 096407 (2008), Phys. Rev. B 79, 161408 (2009)]. These states are of great interest as they constitute a new quasiparticle which is its own antiparticle and can be used as building blocks for fault tolerant topological quantum computing. After an introduction in chapter 1, chapter 2 of the thesis lays the foundation for the understanding of the field of topology in the context of condensed matter physics with a focus on topological band insulators and topological superconductors. Starting from a Chern insulator, the concepts of topological band theory and the bulk boundary corre- spondence are explained. It is then shown that the low energy Hamiltonian of mercury telluride (HgTe) quantum wells of an appropriate thickness can be written as two time reversal symmetric copies of a Chern insulator. This leads to the quantum spin Hall effect. In such a system, spin-polarized one dimensional conducting states form at the edges of the material, while the bulk is insulating. This concept is extended to 3D topological insulators with conducting 2D surface states. As a preliminary step to treating topological superconductivity, a short review of the microscopic theory of superconductivity, i.e. the theory of Bardeen, Cooper, and Shrieffer (BCS theory) is presented. The presence of Majorana end modes in a one dimensional superconducting chain is explained using the Kitaev model. Finally, topological band insulators and conventional superconductivity are combined to effectively engineer p-wave superconductivity. One way to investigate these states is by measuring the periodicity of the phase of the Josephson supercurrent in a topological Josephson junction. The signature is a 4π-periodicity compared to the 2π-periodicity in conventional Josephson junctions. The proof of the presence of this effect in HgTe based Josephson junction is the main goal of this thesis and is discussed in chapters 3 to 6. Chapter 3 describes in detail the transport of a 3D topological insulator based weak link under radio-frequency radiation. The chapter starts with a review of the state of research of (i) strained HgTe as 3D topological insulator and (ii) the progress of induc- ing superconducting correlations into the topological surface states and the theoretical predictions of 3D TI based Josephson junctions. Josephson junctions based on strained HgTe are successfully fabricated. Before studying the ac driven Josephson junctions, the dc transport of the devices is analysed. The critical current as a function of temperature is measured and it is possible to determine the induced superconducting gap. Under rf illumination Shapiro steps form in the current voltage characteristic. A missing first step at low frequencies and low powers is found in our devices. This is a signature of a 4π-periodic supercurrent. By studying the device in a wide parameter range - as a 147148 SUMMARY function of frequency, power, device geometry and magnetic field - it is shown that the results are in agreement with the presence of a single gapless Andreev doublet and several conventional modes. Chapter 4 gives results of the numerical modelling of the I -V dynamics in a Josephson junction where both a 2π- and a 4π-periodic supercurrents are present. This is done in the framework of an equivalent circuit representation, namely the resistively shunted Josephson junction model (RSJ-model). The numerical modelling is in agreement with the experimental results in chapter 3. First, the missing of odd Shapiro steps can be understood by a small 4π-periodic supercurrent contribution and a large number of modes which have a conventional 2π-periodicity. Second, the missing of odd Shapiro steps occurs at low frequency and low rf power. Third, it is shown that stochastic processes like Landau Zener tunnelling are most probably not responsible for the 4π contribution. In a next step the periodicity of Josephson junctions based on quantum spin Hall insulators using are investigated in chapter 5. A fabrication process of Josephson junctions based on inverted HgTe quantum wells was successfully developed. In order to achieve a good proximity effect the barrier material was removed and the superconductor deposited without exposing the structure to air. In a next step a gate electrode was fabricated which allows the chemical potential of the quantum well to be tuned. The measurement of the diffraction pattern of the critical current Ic due to a magnetic field applied perpendicular to the sample plane was conducted. In the vicinity to the expected quantum spin Hall phase, the pattern resembles that of a superconducting quantum interference device (SQUID). This shows that the current flows predominantly on the edges of the mesa. This observation is taken as a proof of the presence of edge currents. By irradiating the sample with rf, missing odd Shapiro steps up to step index n = 9 have been observed. This evidences the presence of a 4π-periodic contribution to the supercurrent. The experiment is repeated using a weak link based on a non-inverted HgTe quantum well. This material is expected to be a normal band insulator without helical edge channels. In this device, all the expected Shapiro steps are observed even at low frequencies and over the whole gate voltage range. This shows that the observed phenomena are directly connected to the topological band structure. Both features, namely the missing of odd Shapiro steps and the SQUID like diffraction pattern, appear strongest towards the quantum spin Hall regime, and thus provide evidence for induced topological superconductivity in the helical edge states. A more direct way to probe the periodicity of the Josephson supercurrent than using Shapiro steps is the measurement of the emitted radiation of a weak link. This experiment is presented in chapter 6. A conventional Josephson junction converts a dc bias V to an ac current with a characteristic Josephson frequency fJ = eV /h. In a topological Josephson junction a frequency at half the Josephson frequency fJ /2 is expected. A new measurement setup was developed in order to measure the emitted spectrum of a single Josephson junction. With this setup the spectrum of a HgTe quantum well based Josephson junction was measured and the emission at half the Josephson frequency fJ /2 was detected. In addition, fJ emission is also detected depending on the gate voltage and detection frequency. The spectrum is again dominated by half the Josephson emission at low voltages while the conventional emission is determines the spectrum at high voltages. A non-inverted quantum well shows only conventional emission over the whole gateSUMMARY 149 voltage and frequency range. The linewidth of the detected frequencies gives a measure on the lifetime of the bound states: From there, a coherence time of 0.3-4ns for the fJ /2 line has been deduced. This is generally shorter than for the fJ line (3-4ns). The last part of the thesis, chapter 7, reports on the induced superconducting state in a strained HgTe layer investigated by point-contact Andreev reflection spectroscopy. For the experiment, a HgTe mesa was fabricated with a small constriction. The diameter of the orifice was chosen to be smaller than the mean free path estimated from magne- totransport measurements. Thus one gets a ballistic point-contact which allows energy resolved spectroscopy. One part of the mesa is covered with a superconductor which induces superconducting correlations into the surface states of the topological insulator. This experiment therefore probes a single superconductor normal interface. In contrast to the Josephson junctions studied previously, the geometry allows the acquisition of energy resolved information of the induced superconducting state through the measurement of the differential conductance dI/dV as a function of applied dc bias for various gate voltages, temperatures and magnetic fields. An induced superconducting order parame- ter of about 70µeV was extracted but also signatures of the niobium gap at the expected value around Δ Nb ≈ 1.1meV have been found. Simulations using the theory developed by Blonder, Tinkham and Klapwijk and an extended model taking the topological surface states into account were used to fit the data. The simulations are in agreement with a small barrier at the topological insulator-induced topological superconductor interface and a high barrier at the Nb to topological insulator interface. To understand the full con- ductance curve as a function of applied voltage, a non-equilibrium driven transformation is suggested. The induced superconductivity is suppressed at a certain bias value due to local electron population. In accordance with this suppression, the relevant scattering regions change spatially as a function of applied bias. To conclude, it is emphasized that the experiments conducted in this thesis found clear signatures of induced topological superconductivity in HgTe based quantum well and bulk devices and opens up the avenue to many experiments. It would be interesting to apply the developed concepts to other topological matter-superconductor hybrid systems. The direct spectroscopy and manipulation of the Andreev bound states using circuit quantum electrodynamic techniques should be the next steps for HgTe based samples. This was already achieved in superconducting atomic break junctions by the group in Saclay [Science 2015, 349, 1199-1202 (2015)]. Another possible development would be the on-chip detection of the emitted spectrum as a function of the phase φ through the junction. In this connection, the topological junction needs to be shunted by a parallel ancillary junction. Such a setup would allow the current phase relation I(φ) directly and the lifetime of the bound states to be measured directly. By coupling this system to a spectrometer, which can be another Josephson junction, the energy dependence of the Andreev bound states E(φ) could be obtained. The experiments on the Andreev reflection spectroscopy described in this thesis could easily be extended to two dimensional topological insulators and to more complex geometries, like a phase bias loop or a tunable barrier at the point-contact. This work might also be useful for answering the question how and why Majorana bound states can be localized in quantum spin Hall systems.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{Schwemmer2023,
  author    = {Schwemmer, Tilman},
  title     = {Relativistic corrections of Fermi surface instabilities},
  doi       = {10.25972/OPUS-31964},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-319648},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {Relativistic effects crucially influence the fundamental properties of many quantum materials. In the accelerated reference frame of an electron, the electric field of the nuclei is transformed into a magnetic field that couples to the electron spin. The resulting interaction between an electron spin and its orbital angular momentum, known as spin-orbit coupling (SOC), is hence fundamental to the physics of many condensed matter phenomena. It is particularly important quantitatively in low-dimensional quantum systems, where its coexistence with inversion symmetry breaking can lead to a splitting of spin degeneracy and spin momentum locking. Using the paradigm of Landau Fermi liquid theory, the physics of SOC can be adequately incorporated in an effective single particle picture. In a weak coupling approach, electronic correlation effects beyond single particle propagator renormalization can trigger Fermi surface instabilities such as itinerant magnetism, electron nematic phases, superconductivity, or other symmetry broken states of matter. In this thesis, we use a weak coupling-based approach to study the effect of SOC on Fermi surface instabilities and, in particular, superconductivity. This encompasses a weak coupling renormalization group formulation of unconventional superconductivity as well as the random phase approximation. We propose a unified formulation for both of these two-particle Green's function approaches based on the notion of a generalized susceptibility. In the half-Heusler semimetal and superconductor LuPtBi, both SOC and electronic correlation effects are prominent, and thus indispensable for any concise theoretical description. The metallic and weakly dispersive surface states of this material feature spin momentum locked Fermi surfaces, which we propose as a possible domain for the onset of unconventional surface superconductivity. Using our framework for the analysis of Fermi surface instability and combining it with ab-initio density functional theory calculations, we analyse the surface band structure of LuPtBi, and particularly its propensity towards Cooper pair formation. We study how the presence of strong SOC modifies the classification of two-electron wave functions as well as the screening of electron-electron interactions. Assuming an electronic mechanism, we identify a chiral superconducting condensate featuring Majorana edge modes to be energetically favoured over a wide range of model parameters.},
  subject      = {Supraleitung},
  language  = {en}
}
@phdthesis{Platt2012,
  author    = {Platt, Christian},
  title     = {A Common Thread in Unconventional Superconductivity: The Functional Renormalization Group in Multi-Band Systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-78824},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {Die supraleitenden Eigenschaften von komplexen Materialsystemen, wie den erst k{\"u}rzlich entdeckten Eisen-Pniktiden oder den Strontium-Ruthenaten, sind oftmals durch das Zusammenspiel vieler elektronischer Orbitale bestimmt. Um die Supraleitung in derartigen Systemen besser zu verstehen, entwickeln wir in dieser Arbeit eine Multi-Orbital-Implementierung der funktionalen Renormierungsgruppe und untersuchen die Elektronenpaarung in verschiedenen charakteristischen Materialverbindungen. In den Eisen-Pniktiden finden wir hierbei mehrere Spinfluktuationskan{\"a}le, die eine Elektronenpaarung hervorrufen, sofern die Paarwellenfunktion einen Vorzeichenwechsel zwischen den verschiedenen genesteten Bereichen der Fermifl{\"a}che aufweist. Abh{\"a}ngig von den spezifischen Materialeigenschaften, wie der Dotierung oder der Position des Pniktogenatoms, f{\"u}hren diese Spinfluktuationen dann zu \$s_{\pm}\$-wellenartiger Paarung mit durchg{\"a}ngiger Energiel{\"u}cke oder mit Knoten auf der Fermifl{\"a}che. In manchen F{\"a}llen wird zudem auch \$d\$-wellenartige Paarung induziert, die in der N{\"a}he des {\"U}bergangs zur \$s_{\pm}\$-Symmetrie einen gemischten \$(s+id)\$-Zustand mit gebrochener Zeitinversionssymmetrie aufweist. Diese neuartige Phase zeigt faszinierende Eigenschaften, wie zum Beispiel das spontane Entstehen von Suprastr{\"o}men am Probenrand und um nichtmagnetische St{\"o}rstellen. Auf Grund der durchg{\"a}ngigen Energiel{\"u}cke ist dieser \$(s+id)\$-Zustand energetisch beg{\"u}nstigt. Im Folgenden untersuchen wir zudem auch die elektronischen Instabilit{\"a}ten eines weiteren außergew{\"o}hnlichen Materials -- dotiertes Graphen. Diese rein zweidimensionale Kohlenstoffverbindung ist schon seit mehreren Jahren im Fokus der Festk{\"o}rperforschung und wurde mittlerweile auch durch neuartige experimentelle Verfahren dotiert, ohne die zugrundeliegende hexagonale Gittersturktur merklich zu st{\"o}ren. Eine theoretische Beschreibung dieses Systems erfordert die Ber{\"u}cksichtigung zweier nicht-equivalenter Gitterpl{\"a}tze, was wiederum effektiv als Zwei-Orbital-System aufgefasst werden kann. Durch die besondere Symmetrie der hexagonalen Gitterstruktur sind beide \$d\$-wellenartigen Paarungskan{\"a}le entartet und ahnlich der \$(s+id)\$-Paarung in den Pniktiden finden wir hier eine chirale \$(d+id)\$-Paarung in einem weiten Dotierungsbereich um van-Hove F{\"u}llung. Des Weiteren identifizieren wir Spin-Triplet-Paarung und eine exotische Form der Spindichtewelle, welche beide durch leichte Ver{\"a}nderung der langreichweitigen H{\"u}pfamplituden und Wechselwirkungensparameter realisiert werden k{\"o}nnen. Als drittes Beispiel betrachten wir die Supraleitung in dem Strontium-Ruthenat Sr\$_2\$RuO\$_4\$. Die Besonderheit dieser Materialverbindung liegt in der m{\"o}glichen Realisierung einer chiralen Spin-Triplet Paarung, die wiederum faszinierende Eigenschaften wie die Existenz von halbganzzahligen Flussvortizes mit nicht-Abelscher Vertauschungsstatistik aufweisen w{\"u}rde. Mittels eines mikroskopischen Drei-Orbital-Modells und der Ber{\"u}cksichtigung von Spin-Bahn-Kopplung finden wir hierbei, dass moderate ferromagnetische Spinfluktuationen immer noch ausreichen, um diesen speziellen Paarungszustand anzutreiben. Die berechnete Energiel{\"u}cke zeigt im Weiteren sehr starke Anisotropien auf dem \$d_{xy}\$-Orbital-dominierten Bereich der Fermifl{\"a}che und verschwindet nahezu vollst{\"a}ndig auf den anderen beiden Fermifl{\"a}chen.},
  subject      = {Supraleitung},
  language  = {en}
}
@phdthesis{Maier2015,
  author    = {Maier, Luis},
  title     = {Induced superconductivity in the topological insulator mercury telluride},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-119405},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {The combination of a topological insulator (TI) and a superconductor (S), which together form a TI/S interface, is expected to influence the possible surface states in the TI. It is of special interest, if the theoretical prediction of zero energy Majorana states in this system is verifiable. This thesis presents the experimental realization of such an interface between the TI strained bulk HgTe and the S Nb and studies if the afore mentioned expectations are met. As these types of interfaces were produced for the first time the initial step was to develop a new lithographic process. Optimization of the S deposition technique as well as the application of cleaning processes allowed for reproducible fabrication of structures. In parallel the measurement setup was upgraded to be able to execute the sensitive measurements at low energy. Furthermore several filters have been implemented into the system to reduce high frequency noise and the magnetic field control unit was additionally replaced to achieve the needed resolution in the μT range. Two kinds of basic geometries have been studied: Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs). A JJ consists of two Nb contacts with a small separation on a HgTe layer. These S/TI/S junctions are one of the most basic structures possible and are studied via transport measurements. The transport through this geometry is strongly influenced by the behavior at the two S/TI interfaces. In voltage dependent differential resistance measurements it was possible to detect multiple Andreev reflections in the JJ, indicating that electrons and holes are able to traverse the HgTe gap between both interfaces multiple times while keeping phase coherence. Additionally using BTK theory it was possible to extract the interface transparency of several junctions. This allowed iterative optimization for the highest transparency via lithographic improvements at these interfaces. The increased transparency and thus the increased coupling of the Nb's superconductivity to the HgTe results in a deeper penetration of the induced superconductivity into the HgTe. Due to this strong coupling it was possible to enter the regime, where a supercurrent is carried through the complete HgTe layer. For the first time the passing of an induced supercurrent through strained bulk HgTe was achieved and thus opened the area for detailed studies. The magnetic dependence of the supercurrent in the JJ was recorded, which is also known as a Fraunhofer pattern. The periodicity of this pattern in magnetic field compared to the JJ geometry allowed to conclude how the junction depends on the phase difference between both superconducting contacts. Theoretical calculations predicted a phase periodicity of 4p instead of 2p, if a TI is used as weak link material between the contacts, due to the presence of Majorana modes. It could clearly be shown that despite the usage of a TI the phase still was 2p periodic. By varying further influencing factors, like number of modes and phase coherence length in the junction, it might still be possible to reach the 4p regime with bound Majorana states in the future. A good candidate for further experiments was found in capped HgTe samples, but here the fabrication process still has to be developed to the same quality as for the uncapped HgTe samples. The second type of geometry studied in this thesis was a DC-SQUID, which consists of two parallel JJs and can also be described as an interference device between two JJs. The DC-SQUID devices were produced in two configurations: The symmetric SQUID, where both JJs were identical, and the asymmetric SQUID, where one JJ was not linear, but instead has a 90° bent. These configurations allow to test, if the predicted uniformity of the superconducting band gap for induced superconductivity in a TI is valid. While the phase of the symmetric SQUID is not influenced by the shape of the band gap, the asymmetric SQUID would be in phase with the symmetric SQUID in case of an uniform band gap and out of phase if p- or d-wave superconductivity is dominating the transport, due to the 90° junction. As both devices are measured one after another, the problem of drift in the coil used to create the magnetic field has to be overcome in order to decide if the oscillations of both types of SQUIDs are in phase. With an oscillation period of 0.5 mT and a drift rate in the range of 5.5 μT/h the measurements on both configurations have to be conducted in a few hours. Only then the total shift is small enough to compare them with each other. For this to be possible a novel measurement system based on a real time micro controller was programmed, which allows a much faster extraction of the critical current of a device. The measurement times were reduced from days to hours, circumventing the drift problems and enabling the wanted comparison. After the final system optimizations it has been shown that the comparison should now be possible. Initial measurements with the old system hinted that both types of SQUIDs are in phase and thus the expected uniform band gap is more likely. With all needed optimizations in place it is now up to the successors of this project to conclusively prove this last point. This thesis has proven that it is possible to induce superconductivity in strained bulk HgTe. It has thus realized the most basic sample geometry proposed by Fu and Kane in 2008 for the appearance of Majorana bound states. Based on this work it is now possible to further explore induced superconductivity in strained bulk HgTe to finally reach a regime, where the Majorana states are both stable and detectable.},
  subject      = {Quecksilbertellurid},
  language  = {en}
}
@phdthesis{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}
}
@phdthesis{Kiesel2012,
  author    = {Kiesel, Maximilian Ludwig},
  title     = {Unconventional Superconductivity in Cuprates, Cobaltates and Graphene: What is Universal and what is Material-Dependent in strongly versus weakly Correlated Materials?},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-76421},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {Eine allgemeing{\"u}ltige Theorie f{\"u}r alle unterschiedlichen Arten von unkonventionellen Supraleitern ist immer noch eine der ungel{\"o}sten Kernfragen der Festk{\"o}rperphysik. Momentan ist es nicht einmal bewiesen, dass es {\"u}berhaupt einen gemeinsamen grundlegenden Mechanismus gibt, sondern es m{\"u}ssen vielleicht mehrere verschiedene Ursachen f{\"u}r unkonventionelle Supraleitung ber{\"u}cksichtigt werden. Der Einfluss der Elektron-Phonon-Wechselwirkung ist dabei noch nicht abschließend gekl{\"a}rt. In dieser Dissertation wird ein rein elektronischer Paarungsmechanismus untersucht, in welchem die Paarung durch Spin-Fluktuationen vermittelt wird, was nach dem aktuellen Stand der Forschung auf dem Gebiet der unkonventionellen Supraleiter am wahrscheinlichsten ist. Der Schwerpunkt liegt dabei auf der Bestimmung von Material-unabh{\"a}ngigen Eigenschaften der supraleitenden Phase. Diese k{\"o}nnen durch eine Auswahl sehr unterschiedlicher Systeme herausgearbeitet werden. Eine Untersuchung der Phasendiagramme gibt außerdem Auskunft dar{\"u}ber, welche konkurrierenden Quantenfluktuationen den supraleitenden Zustand abschw{\"a}chen oder verst{\"a}rken. F{\"u}r diese Analyse von sehr unterschiedlichen supraleitenden Materialien ist der Einsatz einer einzelnen numerischen L{\"o}sungsmethode unzureichend. F{\"u}r diese Dissertation ist dies aber kein Nachteil, sondern vielmehr ein großer Vorteil, da der Einsatz verschiedener Techniken die Abh{\"a}ngigkeit der Ergebnisse von der verwendeten Numerik reduziert und dadurch der grundlegende Mechanismus besser untersucht werden kann. Im speziellen werden in dieser Dissertation die Kuprate mit der Variationellen Clustern{\"a}herung ausgewertet, weil die Elektronen hier eine starke Wechselwirkung untereinander besitzen. Besonders die Frage eines m{\"o}glichen Klebstoffs f{\"u}r die Cooper-Paare wird ausf{\"u}hrlich diskutiert, auch mit einer Unterscheidung in retardierte und nicht-retardierte Betr{\"a}ge. Den Kupraten werden das Kobaltat NaCoO sowie Graphen gegen{\"u}bergestellt. Diese Materialien sind jedoch schwach korrelierte Systeme, so dass hier die Funkionelle Renormierungsgruppe als numerisches Grundger{\"u}st dient. Die Ergebnisse sind reichhaltige Phasendiagramme mit vielen verschiedenen langreichweitigen Ordnungen, wie zum Beispiel d+id-wellenartige Supraleitung. Diese bricht die Zeitumkehr-Symmetrie und besitzt eine vollst{\"a}ndige Bandl{\"u}cke, welche im Falle von NaCoO jedoch eine stark Dotierungs-abh{\"a}ngige Anisotropie aufweist. Als letztes wird das Kagome-Gitter allgemein diskutiert, ohne ein konkretes Material zu beschreiben. Hier hat eine destruktive Interferenz zwischen den Elektronen auf verschiedenen Untergittern drastische Auswirkungen auf die Instabilit{\"a}ten der Fermi-Fl{\"a}che, so dass die {\"u}bliche Spin-Dichte-Welle und die damit verbundene d+id-wellenartige Supraleitung unterdr{\"u}ckt werden. Dadurch treten ungew{\"o}hnliche Spin- und Ladungsdichte-Ordnungen sowie eine nematische Pomeranchuck Instabilit{\"a}t hervor. Zusammengefasst bietet diese Dissertation einen Einblick in unterschiedliche Materialklassen von unkonventionellen Supraleitern. Dadurch wird es m{\"o}glich, die Material-spezifischen Eigenschaften von den universellen zu trennen.},
  subject      = {Supraleitung},
  language  = {en}
}
@phdthesis{Joestingmeier2005,
  author    = {J{\"o}stingmeier, Martin},
  title     = {On the competition of superconductivity, antiferromagnetism and charge order in the high-Tc compounds},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-13036},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {Diese Arbeit l{\"a}ßt sich in zwei grobe Abschnitte gliedern. Der erste Teil umfaßt die Kapitel 1-3, in denen drei verschiedene Konzepte beschrieben werden, die zum Verst{\"a}ndis stark korrelierter Vielteilchen-Systeme dienen. Dies sind zun{\"a}chst einmal die SO(5)-Theorie in Kapitel 3, die den allgemeinen Rahmen vorgibt und auf der numerischen Seite die Stochastische Reihen Entwicklung (SSE) in Kapitel 1 und der Contractor Renormierungsgruppen Ansatz (CORE), s.Kapitel 2). Die zentrale Idee dieser Dissertationsschrift besteht darin, diese verschiedenen Konzepte zu kombinieren, um ein besseres Verst{\"a}ndnis der Hochtemperatursupraleiter zu erhalten. Im zweiten Teil dieser Arbeit (Kap. 4 und Kap. 5) werden die so gewonnenen Ergebnisse dargestellt. Die zentrale Idee dieser Arbeit, d.h. die Kombination der SO(5)-Theorie mit den F{\"a}higkeiten bosonischer Quanten-Monte-Carlo Verfahren und den {\"u}berlegungen der Renormierungsgruppe, hat sich sich am Beispiel der Physik der Hochtemperatur-Supraleiter als sehr tragf{\"a}hig erwiesen. Die numerischen Simulationen reproduzieren bei den behandelten Modelle eine Reihe wichtiger experimenteller Daten. Die Grundlage f{\"u}r eine k{\"u}nftige weitere schrittweise Erweiterung des Modells wurde so geschaffen. Eine offene Frage ist z.B. die Restaurierung der SO(5)-Symmetrie an einem multi-kritischen Punkt, wenn die l{\"a}ngerreichweitigen Wechselwirkungen mit in das Modell einbezogen sind.},
  subject      = {Hochtemperatursupraleitung},
  language  = {en}
}
@phdthesis{Friedrich2023,
  author    = {Friedrich, Felix},
  title     = {Magnetic Excitations in Single and Coupled Atoms on Surfaces: From the Kondo Effect to Yu-Shiba-Rusinov States},
  doi       = {10.25972/OPUS-32069},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-320699},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {Magnetic systems underlie the physics of quantum mechanics when reaching the limit of few or even single atoms. This behavior limits the minimum size of magnetic bits in data storage devices as spontaneous switching of the magnetization leads to the loss of information. On the other hand, exactly these quantum mechanic properties allow to use such systems in quantum computers. Proposals to realize qubits involve the spin states of single atoms as well as topologically protected Majorana zero modes, that emerge in coupled systems of magnetic atoms in proximity to a superconductor. In order to implement and control the proposed applications, a detailed understanding of atomic spins and their interaction with the environment is required. In this thesis, two different systems of magnetic adatoms coupled to metallic and superconducting surfaces are studied by means of scanning tunneling microscopy (STM) and spectroscopy: Co atoms on the clean Cu(111) were among the first systems exhibiting signatures of the Kondo effect in an individual atom. Yet, a recent theoretical work proposed an alternative interpretation of these early experimental results, involving a newly described many-body state. Spin-averaged and -polarized experiments in high magnetic fields presented in this thesis confirm effects beyond the Kondo effect that determine the physics in these Co atoms and suggest a potentially even richer phenomenology than proposed by theory. The second studied system are single and coupled Fe atoms on the superconducting Nb(110) surface. Magnetic impurities on superconducting surfaces locally induce Yu-Shiba-Rusinov (YSR) states inside the superconducting gap due to their pair breaking potential. Coupled systems of such impurities exhibit YSR bands and, if the bands cross the Fermi level such that the band structure is inverted, host Majorana zero modes. Using the example of Fe atoms on Nb(110), the YSR states' dependence on the adatom-substrate interaction as well as the interatomic YSR state coupling is investigated. In the presence of oxygen on the Nb surface, the adatom-substrate interaction is shown to be heavily modified and the YSR states are found to undergo a quantum phase transition, which can be directly linked to a modified Kondo screening. STM tips functionalized with CO molecules allow to resolve self-assembled one-dimensional chains of Fe atoms on the clean Nb(110) surface to study the YSR states' coupling. Mapping out the states' wave functions reveals their symmetry, which is shown to alter as a function of the states' energy and number of atoms in the chain. These experimental results are reproduced in a simple tight-binding model, demonstrating a straightforward possibility to describe also more complex YSR systems toward engineered, potentially topologically non-trivial states.},
  subject      = {Rastertunnelmikroskopie},
  language  = {en}
}
@phdthesis{Fleckenstein2020,
  author    = {Fleckenstein, Christoph Thomas},
  title     = {Conception and detection of exotic quantum matter in mesoscopic systems},
  doi       = {10.25972/OPUS-21284},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-212847},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {In this thesis we discuss the potential of nanodevices based on topological insulators. This novel class of matter is characterized by an insulating bulk with simultaneously conducting boundaries. To lowest order, the states that are evoking the conducting behavior in TIs are typically described by a Dirac theory. In the two-dimensional case, together with time- reversal symmetry, this implies a helical nature of respective states. Then, interesting physics appears when two such helical edge state pairs are brought close together in a two-dimensional topological insulator quantum constriction. This has several advantages. Inside the constriction, the system obeys essentially the same number of fermionic fields as a conventional quantum wire, however, it possesses more symmetries. Moreover, such a constriction can be naturally contacted by helical probes, which eventually allows spin- resolved transport measurements. We use these intriguing properties of such devices to predict the formation and detection of several profound physical effects. We demonstrate that narrow trenches in quantum spin Hall materials - a structure we coin anti-wire - are able to show a topological super- conducting phase, hosting isolated non-Abelian Majorana modes. They can be detected by means of a simple conductance experiment using a weak coupling to passing by helical edge states. The presence of Majorana modes implies the formation of unconventional odd-frequency superconductivity. Interestingly, however, we find that regardless of the presence or absence of Majoranas, related (superconducting) devices possess an uncon- ventional odd-frequency superconducting pairing component, which can be associated to a particular transport channel. Eventually, this enables us to prove the existence of odd- frequency pairing in superconducting quantum spin Hall quantum constrictions. The symmetries that are present in quantum spin Hall quantum constrictions play an essen- tial role for many physical effects. As distinguished from quantum wires, quantum spin Hall quantum constrictions additionally possess an inbuilt charge-conjugation symmetry. This can be used to form a non-equilibrium Floquet topological phase in the presence of a time-periodic electro-magnetic field. This non-equilibrium phase is accompanied by topological bound states that are detectable in transport characteristics of the system. Despite single-particle effects, symmetries are particularly important when electronic in- teractions are considered. As such, charge-conjugation symmetry implies the presence of a Dirac point, which in turn enables the formation of interaction induced gaps. Unlike single-particle gaps, interaction induced gaps can lead to large ground state manifolds. In combination with ordinary superconductivity, this eventually evokes exotic non-Abelian anyons beyond the Majorana. In the present case, these interactions gaps can even form in the weakly interacting regime (which is rather untypical), so that the coexistence with superconductivity is no longer contradictory. Eventually this leads to the simultaneous presence of a Z4 parafermion and a Majorana mode bound at interfaces between quantum constrictions and superconducting regions.},
  subject      = {Kondensierte Materie},
  language  = {en}
}
@phdthesis{Breunig2021,
  author    = {Breunig, Daniel Manfred},
  title     = {Transport properties and proximity effect of topological hybrid structures},
  doi       = {10.25972/OPUS-25054},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-250546},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {Over the last two decades, accompanied by their prediction and ensuing realization, topological non-trivial materials like topological insulators, Dirac semimetals, and Weyl semimetals have been in the focus of mesoscopic condensed matter research. While hosting a plethora of intriguing physical phenomena all on their own, even more fascinating features emerge when superconducting order is included. Their intrinsically pronounced spin-orbit coupling leads to peculiar, time-reversal symmetry protected surface states, unconventional superconductivity, and even to the emergence of exotic bound states in appropriate setups. This Thesis explores various junctions built from - or incorporating - topological materials in contact with superconducting order, placing particular emphasis on the transport properties and the proximity effect. We begin with the analysis of Josephson junctions where planar samples of mercury telluride are sandwiched between conventional superconducting contacts. The surprising observation of pronounced excess currents in experiments, which can be well described by the Blonder-Tinkham-Klapwijk theory, has long been an ambiguous issue in this field, since the necessary presumptions are seemingly not met. We propose a resolution to this predicament by demonstrating that the interface properties in hybrid nanostructures of distinctly different materials yet corroborate these assumptions and explain the outcome. An experimental realization is feasible by gating the contacts. We then proceed with NSN junctions based on time-reversal symmetry broken Weyl semimetals and including superconducting order. Due to the anisotropy of the electron band structure, both the transport properties as well as the proximity effect depend substantially on the orientation of the interfaces between the materials. Moreover, an imbalance can be induced in the electron population between Weyl nodes of opposite chirality, resulting in a non-vanishing spin polarization of the Cooper pairs leaking into the normal contacts. We show that such a system features a tunable dipole character with possible applications in spintronics. Finally, we consider partially superconducting surface states of three-dimensional topological insulators. Tuning such a system into the so-called bipolar setup, this results in the formation of equal-spin Cooper pairs inside the superconductor, while simultaneously acting as a filter for non-local singlet pairing. The creation and manipulation of these spin-polarized Cooper pairs can be achieved by mere electronic switching processes and in the absence of any magnetic order, rendering such a nanostructure an interesting system for superconducting spintronics. The inherent spin-orbit coupling of the surface state is crucial for this observation, as is the bipolar setup which strongly promotes non-local Andreev processes.},
  subject      = {Supraleitung},
  language  = {en}
}