@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{Schuetz2020,
  author    = {Sch{\"u}tz, Philipp},
  title     = {Dimensionality-Driven Metal-Insulator Transition in Spin-Orbit-Coupled SrIrO\(_3\)},
  doi       = {10.25972/OPUS-21278},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-212781},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {In the past decades correlated-electron physics due to strong Coulomb interactions and topological physics caused by band inversion often induced by strong spin-orbit coupling have been the workhorses of solid state research. While commonly considered as disparate phenomena, it was realized in the early 2010s that the interplay between the comparably strong Coulomb and spin-orbit interactions in the \$5d\$ transition metal oxides may result in hitherto unforeseen properties. The layered perovskite Sr\$\textsubscript{2}\$IrO\$\textsubscript{4}\$ has attracted special attention due to the observation of an unconventional Mott-insulating phase and predictions of exotic superconductivity. Less is known about its three-dimensional counterpart SrIrO\$\textsubscript{3}\$, since rather than the cubic perovskite structure it adopts the thermodynamically stable hexagonal polymorph thereof. This thesis therefore sets out to establish the synthesis of epitaxially stabilized perovskite SrIrO\$\textsubscript{3}\$ by pulsed laser deposition and to investigate its electronic and magnetic structure by state-of-the-art x-ray spectroscopy techniques. In this endeavor the appropriate thermodynamic conditions for the growth of high-quality SrIrO\$\textsubscript{3}\$ are identified with a focus on the prevention of cation off-stoichiometry and the sustainment of layer-by-layer growth. In the thus-optimized films the cubic perovskite symmetry is broken by a tetragonal distortion due to epitaxial strain and additional cooperative rotations of the IrO\$\textsubscript{6}\$ octahedra. As a consequence of the thermodynamic instability of the IrO\$\textsubscript{2}\$ surface layer, the films unexpectedly undergo a conversion to a SrO termination during growth. In an attempt to disentangle the interplay between spin-orbit and Coulomb interaction the three-dimensional electronic structure of perovskite SrIrO\$\textsubscript{3}\$ is investigated in a combined experimental and theoretical approach using soft x-ray angle-resolved photoelectron spectroscopy and \textit{ab initio} density functional theory calculations. The experimentally found metallic ground state hosts coherent quasiparticle peaks with a well-defined Fermi surface and is theoretically described by a single half-filled band with effective total angular momentum \$J_\text{eff} = 1/2\$ only upon incorporation of a sizeable local Coulomb repulsion and -- to a lesser extent -- the broken cubic crystal symmetry in the film. Upon reduction of the SrIrO\$\textsubscript{3}\$ thickness below a threshold of four unit cells the scales are tipped in favor of a Mott-insulating phase as the on-site Coulomb repulsion surmounts the diminishing kinetic energy upon transition into the two-dimensional regime. Concomitantly, a structural transition occurs because the corner-shared octahedral network between substrate and film imposes constraints upon the IrO\$\textsubscript{6}\$ octahedral rotations in the thin-film limit. The striking similarity between the quasi-two-dimensional spin-orbit-induced Mott insulator Sr\$\textsubscript{2}\$IrO\$\textsubscript{4}\$ and SrO-terminated SrIrO\$\textsubscript{3}\$ in the monolayer limit underlines the importance of dimensionality for the metal-insulator transition and possibly opens a new avenue towards the realization of exotic superconductivity in iridate compounds. Whether the analogy between SrIrO\$\textsubscript{3}\$ in the two-dimensional limit and its Ruddlesden-Popper bulk counterparts extends to their complex magnetic properties ultimately remains an open question, although no indications for a remanent (anti)ferromagnetic order were found. The unprecedented observation of an x-ray magnetic circular dichroism at the O~\$K\$-absorption edge of iridium oxides in an external magnetic field promises deeper insights into the intricate connection between the \$J_\text{eff} = 1/2\$ pseudospin state, its hybridization with the oxygen ligand states and the magnetic order found in the Ruddlesden-Popper iridates.},
  subject      = {Festk{\"o}rperphysik},
  language  = {en}
}
@phdthesis{Elsaesser2019,
  author    = {Els{\"a}sser, Sebastian},
  title     = {Lattice dynamics and spin-phonon coupling in the multiferroic oxides Eu(1-x)Ho(x)MnO3 and ACrO2},
  doi       = {10.25972/OPUS-17971},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-179719},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {The focus of this thesis is the investigation of the lattice dynamics and the coupling of magnetism and phonons in two different multiferroic model systems. The first system, which constitutes the main part in this work is the system of multiferroic manganites RMnO\$_{3}\$, in particular Eu\$_{1-x}\$Ho\$_{x}\$MnO\$_{3}\$ with \$0 \le x \le 0.5\$. Its cycloidal spin arrangement leads to the emergence of the ferroelectric polarization via the inverse Dzyaloshinskii-Moriya interaction. This system is special among RMnO\$_{3}\$ as with increasing Ho content \$x\$, Eu\$_{1-x}\$Ho\$_{x}\$MnO\$_{3}\$ does not only become multiferroic, but due to the exchange interaction with the magnetic Ho-ion, the spin cycloid (and with it the electric polarization) is also flipped for higher Ho contents. This makes it one of the first compounds, where the cycloidal reorientation happens spontaneously, rather than with the application of external fields. On the other hand, there is the delafossite ACrO\$_{2}\$ system. Here, due to symmetry reasons, the spin-spiral pattern can not induce the polarization according to the inverse Dzyaloshinskii-Moriya interaction mechanism. Instead, it is thought that another way of magnetoelectric coupling is involved, which affects the charge distribution in the \$d-p\$ hybridized orbitals of the bonds. The lattice vibrations as well as the quasi-particle of the multiferroic phase, the electromagnon, are studied by Raman spectroscopy. Lattice vibrations like the B\$_{3g}\$(1) mode, which involves vibrations of the Mn-O-Mn bonds modulate the exchange interaction and serve as a powerful tool for the investigation of magnetic correlations effects with high frequency accuracy. Raman spectroscopy acts as a local probe as even local magnetic correlations directly affect the phonon vibration frequency, revealing coupling effects onto the lattice dynamics even in the absence of global magnetic order. By varying the temperature, the coupling is investigated and unveils a renormalization of the phonon frequency as the magnetic order develops. For Eu\$_{1-x}\$Ho\$_{x}\$MnO\$_{3}\$, the analysis of this spin-induced phonon frequency renormalization enables the quantitative determination of the in-plane spin-phonon coupling strengths. This formalism, introduced by Granado et al., is extended here to evaluate the out-of-plane coupling strengths, which is enabled by the identification of a previously elusive feature as a vibrational mode. The complete picture is obtained by studying the lattice- and electromagnon dynamics in the magnetic field. Further emphasis is put towards the development of the cycloidal spin structure and correlations with temperature. A new model of describing the temperature-dependent behavior of said spin correlations is proposed and can consistently explain ordering phenomena which were until now unaddressed. The results are underscored with Monte Carlo based simulations of the spin dynamics with varying temperature. Furthermore, a novel effect of a tentative violation of the Raman selection rules in Eu\$_{1-x}\$Ho\$_{x}\$MnO\$_{3}\$ was discovered. While the phonon modes can be separated and identified by their symmetry by choosing appropriate polarization configurations, in a very narrow temperature range, Eu\$_{1-x}\$Ho\$_{x}\$MnO\$_{3}\$ shows an increase of phonon intensities in polarization configurations where they should be forbidden. This is interpreted as a sign of local disorder, caused by 90° domain walls and could be explained within the model framework. This course of action is followed with the material system of delafossites ACrO\$_{2}\$. Being a relatively new class of multiferroic materials, the investigations on ACrO\$_{2}\$ are also of characterizing nature. For this, shell model calculations are performed as a reference to compare the vibrational frequencies obtained by the Raman experiments to. A renormalization of the vibrational frequencies is observed in this system as well and systematically analyzed across the sample series of \textit{A}=Cu, Pd and Ag. Eventually, the effect of applying an external magnetic field is studied. A particularly interesting feature specific for CuCrO\$_{2}\$ is a satellite peak which appears at lower temperatures. It is presumably related to a deformation of the lattice and therefore going to be discussed in further detail.},
  subject      = {Festk{\"o}rperphysik},
  language  = {en}
}
@phdthesis{Huewe2017,
  author    = {H{\"u}we, Florian},
  title     = {Electrothermal Investigation on Charge and Heat Transport in the Low-Dimensional Organic Conductor (DCNQI)\(_2\)Cu},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-153492},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2017},
  abstract  = {This thesis aimed at the coherent investigation of the electrical and thermal transport properties of the low-dimensional organic conductor (DCNQI)2M (DCNQI: dicyanoquinonediimine; M: metallic counterion). These radical anion salts present a promising, new material class for thermoelectric applications and hence, a consistent characterization of the key parameters is required to evaluate and to optimize their performance. For this purpose, a novel experimental measurement setup enabling the determination of the electrical conductivity, the Seebeck coefficient and the thermal conductivity on a single crystalline specimen has been designed and implemented in this work. The novel measurement setup brought to operation within this thesis enabled a thorough investigation of the thermal transport properties in the (DCNQI)2M system. The thermal conductivity of (DCNQI-h8)2Cu at RT was determined to κ=1.73 W m^(-1) K^(-1). By reducing of the copper content in isostructural, crystalline (DMe-DCNQI)2CuxLi1-x alloys, the electrical conductivity has been lowered by one order of magnitude and the correlated changes in the thermal conductivity allowed for a verification of the Wiedemann-Franz (WF) law at RT. A room temperature Lorenz number of L=(2.48±0.45)⋅〖10〗^(-8) WΩK^(-2) was obtained in agreement with the standard Lorenz number L_0=2,44⋅〖10〗^(-8) WΩK^(-2) for 3D bulk metals. This value appears to be significantly reduced upon cooling below RT, even far above the Debye temperature of θ_D≈82 K, below which a breakdown of the WF law is caused by different relaxation times in response to thermal and to electric field perturbations. The experimental data enabled the first consistent evaluation of the thermoelectric performance of (DCNQI)\$_2\$Cu. The RT power factor of 110 μWm^(-1) K^(-2) is comparable to values obtained on PEDOT-based thermoelectric polymers. The RT figure of merit amounts to zT=0.02 which falls short by a factor of ten compared to the best values of zT=0.42 claimed for conducting polymers. It originates from the larger thermal conductivity in the organic crystals of about 1.73 W m^(-1) K^(-1) in (DCNQI)2Cu. Yet, more elaborate studies on the anisotropy of the thermal conductivity in PEDOT polymers assume their figure of merit to be zT=0.15 at most, recently. Therefore, (DCNQI)2Cu can be regarded as thermoelectric material of similar performance to polymer-based ones. Moreover, it represents one of the best organic n-type thermoelectric materials to date and as such, may also become important in hybrid thermoelectrics in combination with conducting polymers. Upon cooling below room temperature, (DCNQI)2Cu reveals its full potential attaining power factors of 50 mW K^(-2) m^(-1) and exceeding values of zT>0.15 below 40 K. These values represent the best thermoelectric performance in this low-temperature regime for organic as well as inorganic compounds and thus, low-dimensional organic conductors might pave the way toward new applications in cryogenic thermoelectrics. Further improvements may be expected from optimizing the charge carrier concentration by taking control over the CT process via the counterion stack of the crystal lattice. The concept has also been demonstrated in this work. Moreover, the thermoelectric performance in the vicinity of the CDW transition in (MeBr-DCNQI)2Cu was found to be increased by a factor of 5. Accordingly, the diversity of electronic ground states accessible in organic conductors provides scope for further improvements. Finally, the prototype of an all-organic thermoelectric generator has been built in combination with the p-type organic metal TTT2I3. While it only converts about 0.02\% of the provided heat into electrical energy, the specific power output per active area attains values of up to 5 mW cm^(-2). This power output, defining the cost-limiting factor in the recovery of waste heat, is three orders of magnitude larger than in conducting polymer devices and as such, unrivaled in organic thermoelectrics. While the thermoelectric key parameters of (DCNQI)2Cu still lack behind conventional thermoelectrics made of e.g. Bi2Te3, the promising performance together with its potential for improvements make this novel material class an interesting candidate for further exploration. Particularly, the low-cost and energy-efficient synthesis routes of organic materials highlight their relevance for technological applications.},
  subject      = {Radikalanionensalz},
  language  = {en}
}
@phdthesis{Fuchs2016,
  author    = {Fuchs, Moritz Jakob},
  title     = {Spin dynamics in the central spin model: Application to graphene quantum dots},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-136079},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {Due to their potential application for quantum computation, quantum dots have attracted a lot of interest in recent years. In these devices single electrons can be captured, whose spin can be used to define a quantum bit (qubit). However, the information stored in these quantum bits is fragile due to the interaction of the electron spin with its environment. While many of the resulting problems have already been solved, even on the experimental side, the hyperfine interaction between the nuclear spins of the host material and the electron spin in their center remains as one of the major obstacles. As a consequence, the reduction of the number of nuclear spins is a promising way to minimize this effect. However, most quantum dots have a fixed number of nuclear spins due to the presence of group III and V elements of the periodic table in the host material. In contrast, group IV elements such as carbon allow for a variable size of the nuclear spin environment through isotopic purification. Motivated by this possibility, we theoretically investigate the physics of the central spin model in carbon based quantum dots. In particular, we focus on the consequences of a variable number of nuclear spins on the decoherence of the electron spin in graphene quantum dots. Since our models are, in many aspects, based upon actual experimental setups, we provide an overview of the most important achievements of spin qubits in quantum dots in the first part of this Thesis. To this end, we discuss the spin interactions in semiconductors on a rather general ground. Subsequently, we elaborate on their effect in GaAs and graphene, which can be considered as prototype materials. Moreover, we also explain how the central spin model can be described in terms of open and closed quantum systems and which theoretical tools are suited to analyze such models. Based on these prerequisites, we then investigate the physics of the electron spin using analytical and numerical methods. We find an intriguing thermal flip of the electron spin using standard statistical physics. Subsequently, we analyze the dynamics of the electron spin under influence of a variable number of nuclear spins. The limit of a large nuclear spin environment is investigated using the Nakajima-Zwanzig quantum master equation, which reveals a decoherence of the electron spin with a power-law decay on short timescales. Interestingly, we find a dependence of the details of this decay on the orientation of an external magnetic field with respect to the graphene plane. By restricting to a small number of nuclear spins, we are able to analyze the dynamics of the electron spin by exact diagonalization, which provides us with more insight into the microscopic details of the decoherence. In particular, we find a fast initial decay of the electron spin, which asymptotically reaches a regime governed by small fluctuations around a finite long-time average value. Finally, we analytically predict upper bounds on the size of these fluctuations in the framework of quantum thermodynamics.},
  subject      = {Elektronenspin},
  language  = {en}
}
@phdthesis{Posske2015,
  author    = {Posske, Thore Hagen},
  title     = {Dressed Topological Insulators: Rashba Impurity, Kondo Effect, Magnetic Impurities, Proximity-Induced Superconductivity, Hybrid Systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-131249},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Topological insulators are electronic phases that insulate in the bulk and accommodate a peculiar, metallic edge liquid with a spin-dependent dispersion. They are regarded to be of considerable future use in spintronics and for quantum computation. Besides determining the intrinsic properties of this rather novel electronic phase, considering its combination with well-known physical systems can generate genuinely new physics. In this thesis, we report on such combinations including topological insulators. Specifically, we analyze an attached Rashba impurity, a Kondo dot in the two channel setup, magnetic impurities on the surface of a strong three-dimensional topological insulator, the proximity coupling of the latter system to a superconductor, and hybrid systems consisting of a topological insulator and a semimetal. Let us summarize our primary results. Firstly, we determine an analytical formula for the Kondo cloud and describe its possible detection in current correlations far away from the Kondo region. We thereby rely on and extend the method of refermionizable points. Furthermore, we find a class of gapless topological superconductors and semimetals, which accommodate edge states that behave similarly to the ones of globally gapped topological phases. Unexpectedly, we also find edge states that change their chirality when affected by sufficiently strong disorder. We regard the presented research helpful in future classifications and applications of systems containing topological insulators, of which we propose some examples.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Thienel2015,
  author    = {Thienel, Cornelius},
  title     = {Exploring the transport properties of the three-dimensional topological insulator material HgTe},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-122031},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {In der vorliegenden Dissertation werden die Transporteigenschaften von verspannten HgTe-Volumenkristallen untersucht. Verspanntes HgTe stellt einen dreidimensionalen topologischen Isolator dar und ist zur Erkundung von topologischen Oberfl{\"a}chenzust{\"a}nden von speziellem Interesse, da es mit Hilfe von Molekularstrahlepitaxie in hoher Kristallqualit{\"a}t gewachsen werden kann. Die niedrige Defektdichte f{\"u}hrt zu beachtlichen Ladungstr{\"a}gerbeweglichkeiten, die deutlich {\"u}ber denen anderer topologischer Isolatoren liegen. Verspanntes HgTe hat jedoch eine kleine Energiel{\"u}cke von ca. 20 meV. Deshalb ist es f{\"u}r eine m{\"o}gliche Verwendung des Materials ein wichtiger Aspekt, in welchem Parameterbereich Oberfl{\"a}chentransport stattfindet. Um dieser Frage nachzugehen, werden die HgTe-Proben bei tiefen Temperaturen (T < 100 mK) und unter dem Einfluss hoher Magnetfelder in verschiedenen Orientierungen untersucht. Der Einfluss von Gate-Elektroden ober- und unterhalb der Struktur sowie von Deckschichten, die die Oberfl{\"a}chen sch{\"u}tzen, wird diskutiert. Basierend auf einer Analyse des Quanten-Hall-Effekts wird gezeigt, dass der Transport in diesem Material von topologischen Oberfl{\"a}chenzust{\"a}nden dominiert ist. Die Abh{\"a}ngigkeit der topologischen Oberfl{\"a}chenzust{\"a}nde von der Gate-Spannung wird dargestellt. Durch diese Abh{\"a}ngigkeit ist es zum ersten Mal m{\"o}glich, eine ungerade ganzzahlige Quanten-Hall-Plateau Sequenz nachzuweisen, die von den Oberfl{\"a}chen senkrecht zum Magnetfeld stammt. Des Weiteren wird im Rahmen dieser Arbeit in Proben hoher Oberfl{\"a}chenqualit{\"a}t zum ersten Mal f{\"u}r einen 3D TI der p-Typ QHE der Oberfl{\"a}chenzust{\"a}nde beobachtet. Aus der Gate-Abh{\"a}ngigkeit der Messungen wird geschlossen, dass das Abschirmverhalten in 3D TIs nicht trivial ist. Die Transportdaten werden mit Hilfe von intuitiven theoretischen Modellen auf qualitative Weise analysiert.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Goth2015,
  author    = {Goth, Florian},
  title     = {Continuous time quantum Monte Carlo Studies of Quenches and Correlated Systems with Broken Inversion Symmetry},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-118836},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {This thesis deals with quantum Monte Carlo simulations of correlated low dimensional electron systems. The correlation that we have in mind is always given by the Hubbard type electron electron interaction in various settings. To facilitate this task, we develop the necessary methods in the first part. We develop the continuous time interaction expansion quantum algorithm in a manner suitable for the treatment of effective and non-equilibrium problems. In the second part of this thesis we consider various applications of the algorithms. First we examine a correlated one-dimensional chain of electrons that is subject to some form of quench dynamics where we suddenly switch off the Hubbard interaction. We find the light-cone-like Lieb-Robinson bounds and forms of restricted equilibration subject to the conserved quantities. Then we consider a Hubbard chain subject to Rashba spin-orbit coupling in thermal equilibrium. This system could very well be realized on a surface with the help of metallic adatoms. We find that we can analytically connect the given model to a model without spin-orbit coupling. This link enabled us to interpret various results for the standard Hubbard model, such as the single-particle spectra, now in the context of the Hubbard model with Rashba spin-orbit interaction. And finally we have considered a magnetic impurity in a host consisting of a topological insulator. We find that the impurity still exhibits the same features as known from the single impurity Anderson model. Additionally we study the effects of the impurity in the bath and we find that in the parameter regime where the Kondo singlet is formed the edge state of the topological insulator is rerouted around the impurity.},
  subject      = {Elektronenkorrelation},
  language  = {en}
}
@phdthesis{Schelter2012,
  author    = {Schelter, J{\"o}rg},
  title     = {The Aharonov-Bohm effect and resonant scattering in graphene},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-74662},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {In this thesis, the electronic transport properties of mesoscopic condensed matter systems based on graphene are investigated by means of numerical as well as analytical methods. In particular, it is analyzed how the concepts of quantum interference and disorder, which are essential to mesoscopic devices in general, are affected by the unique electronic and transport properties of the graphene material system. We consider the famous Aharonov-Bohm effect in ring-shaped transport geometries, and, besides providing an overview over the recent developments on the subject, we study the signatures of fundamental phenomena such as Klein tunneling and specular Andreev reflection, which are specific to graphene, in the magnetoconductance oscillations. To this end, we introduce and utilize a variant of the well-known recursive Green's function technique, which is an efficient numerical method for the calculation of transport observables in effectively non-interacting open quantum systems in the framework of a tight binding model. This technique is also applied to study the effects of a specific kind of disorder, namely short-range resonant scatterers, such as strongly bound adatoms or molecules, that can be modeled as vacancies in the graphene lattice. This numerical analysis of the conductance in the presence of resonant scatterers in graphene leads to a non-trivial classification of impurity sites in the graphene lattice and is further substantiated by an independent analytical treatment in the framework of the Dirac equation. The present thesis further contains a formal introduction to the topic of non-equilibrium quantum transport as appropriate for the development of the numerical technique mentioned above, a general introduction to the physics of graphene with a focus on the particular phenomena investigated in this work, and a conclusion where the obtained results are summarized and open questions as well as potential future developments are highlighted.},
  subject      = {Graphen},
  language  = {en}
}