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Institut
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.
Quantitative Electron Paramagnetic Resonance Studies of Charge Transfer in Organic Semiconductors
(2020)
In the present work we investigated various charge transfer processes, as they appear in the versatile world of organic semiconductors by probing the spin states of the corresponding charge carrier species via electron paramagnetic resonance (EPR) spectroscopy. All studied material systems are carbon-based compounds, either belonging to the group of polymers, fullerenes, or single-wall carbon nanotubes (SWNTs).
In the first instance, we addressed the change of the open circuit voltage (Voc) with the fullerene blend stoichiometry in fullerene-based solar cells for organic photovoltaics (OPV). The voltage depends strongly on the energy separation between the lowest unoccupied molecular orbital (LUMO) of the donor and the highest occupied molecular orbital (HOMO) of the acceptor. By exploiting the Gaussian distribution of the charge carriers in a two-level system, and thus also their spins in the EPR experiment, it could be shown that the LUMOs get closer by a few to a few hundred meV when going from pure fullerene materials to a fullerene mixture. The reason for this strong energetic effect is likely the formation of a fullerene alloy.
Further, we investigated the chemical doping mechanism of SWNTs with a (6,5)-chirality and their behaviour under optical excitation. In order to determine the unintentional (pre)-doping of SWNTs, EPR spectra of the raw material as well as after different purification steps were recorded. This facilitated the determination of nanotube defects and atmospheric p-doping as the causes of the measured EPR signals. In order to deliberately transfer additional charge carriers to the nanotubes, we added the redox-active substance AuCl3 where we determined an associated doping-yield of (1.5±0.2)%. In addition, a statistical occupation model was developed which can be used to simulate the distribution of EPR active, i.e. unpaired and localised charge carriers on the nanotubes.
Finally, we investigated the charge transfer behaviour of (6,5)-SWNTs together with the polymer P3HT and the fullerene PC60BM after optical excitation.
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.
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.
The AdS/CFT correspondence is an explicit realization of the holographic principle. It describes a field theory living on the boundary of a volume by a gravitational theory living in the interior and vice-versa. With its origins in string theory, the correspondence incorporates an explicit relationship between the degrees of freedom of both theories: the AdS/CFT dictionary. One astonishing aspect of the AdS/CFT correspondence is the emergence of geometry from field theory.
On the gravity side, a natural way to probe the geometry is to study boundary-anchored extremal surfaces of different dimensionality. While there is no unified way to determine the field theory dual for such non-local quantities, the AdS/CFT dictionary contains entries for surfaces of certain dimensionality: it relates two-point functions to geodesics, the Wilson loop expectation value to two-dimensional surfaces and the entanglement entropy, i.e. a measure for entanglement between states in a region and in its complement, to co-dimension two surfaces in the bulk.
In this dissertation, we calculate these observables for gravity setups dual to thermal states in the field theory. The geometric dual is given by AdS Schwarzschild black holes in general dimensions. We find analytic results for minimal areas in this setup. One focus of our analysis is the high-temperature limit. The leading and subleading term in this limit have diverse interpretation for the different observables. For example, the subleading term of the entanglement entropy satisfies a c-theorem for renormalization flows and gives insights into the number of effective degrees of freedom.
The entanglement entropy emerged as the favorable way to probe the geometric dual. In addition to the extremal bulk surface, the holographic entanglement entropy associates a bulk region to the considered boundary region. The volume of this region is conjectured to be a measure of complexity, i.e. a measure of how difficult it is to obtain the corresponding field-theory state. Building on our aforementioned results for the entanglement entropy, we study this complexity for AdS Schwarzschild black holes in general dimensions.
In particular, we draw conclusions on how efficient holography encodes the field theory and compare these results to MERA tensor networks, a numerical tool to study quantum many-body systems.
Moreover, we holographically study the complexity of pure states. This sheds light on the notion of complexity in field theories. We calculate the complexity for a simple, calculable example: states obtained by conformal transformations of the vacuum state in AdS3/CFT2. In this lower-dimensional realization of AdS/CFT, the conformal group is infinite dimensional. We construct a continuous space of states with the same complexity as the vacuum state. Furthermore, we determine the change of complexity caused by small conformal transformation. The field-theory operator implementing this transformation is known and allows to compare the holographic results to field theory expectations.
In this thesis we consider the hybrid quantum Monte Carlo method for simulations of the Hubbard and Su-Schrieffer-Heeger model. In the first instance, we discuss the hybrid quantum Monte Carlo method for the Hubbard model on a square lattice. We point out potential ergodicity issues and provide a way to circumvent them by a complexification of the method. Furthermore, we compare the efficiency of the hybrid quantum Monte Carlo method with a well established determinantal quantum Monte Carlo method for simulations of the half-filled Hubbard model on square lattices. One reason why the hybrid quantum Monte Carlo method loses the comparison is that we do not observe the desired sub-quadratic scaling of the numerical effort. Afterwards we present a formulation of the hybrid quantum Monte Carlo method for the Su-Schrieffer-Heeger model in two dimensions. Electron-phonon models like this are in general very hard to simulate using other Monte Carlo methods in more than one dimensions. It turns out that the hybrid quantum Monte Carlo method is much better suited for this model . We achieve favorable scaling properties and provide a proof of concept. Subsequently, we use the hybrid quantum Monte Carlo method to investigate the Su-Schrieffer-Heeger model in detail at half-filling in two dimensions. We present numerical data for staggered valence bond order at small phonon frequencies and an antiferromagnetic order at high frequencies. Due to an O(4) symmetry the antiferromagnetic order is connected to a superconducting charge density wave. Considering the Su-Schrieffer-Heeger model without tight-binding hopping reveals an additional unconstrained Z_2 gauge theory. In this case, we find indications for π-fluxes and a possible Z_2 Dirac deconfined phase as well as for a columnar valence bond ordered state at low phonon energies. In our investigations of the several phase transitions we discuss the different possibilities for the underlying mechanisms and reveal first insights into a rich phase diagram.