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Die Dissertation beschäftigt sich mit der Analyse von oxidischen Nanostrukturen. Die Grundlage der Bauelemente stellt dabei die LaAlO3/SrTiO3-Heterostruktur dar. Hierbei entsteht an der Grenzfläche beider Übergangsmetalloxide ein quasi zweidimensionales Elektronengas, welches wiederum eine Fülle von beachtlichen Eigenschaften und Charakteristika zeigt. Mithilfe lithographischer Verfahren wurden zwei unterschiedliche Bauelemente verwirklicht. Dabei handelt es sich einerseits um einen planaren Nanodraht mit lateralen Gates, welcher auf der Probenoberfläche prozessiert wurde und eine bemerkenswerte Trialität aufweist. Dieses Bauelement kann unter anderem als ein herkömmlicher Feldeffekttransistor agieren, wobei der Ladungstransport durch die lateral angelegte Spannung manipuliert wird. Zusätzlich konnten auch Speichereigenschaften beobachtet werden, sodass das gesamte Bauelement als ein sogenannter Memristor fungieren kann. In diesem Fall hängt der Ladungstransport von der Elektronenakkumulation auf den lateralen potentialfreien Gates ab. Die Memristanz des Nanodrahts lässt sich unter anderem durch Lichtleistungen im Nanowattbereich und mithilfe von kurzen Spannungspulsen verändern. Darüber hinaus kann die Elektronenakkumulation auch in Form einer memkapazitiven Charakteristik beobachtet werden. Neben dem Nanodraht wurde auch eine Kreuzstruktur, die eine ergänzende ferromagnetischen Elektrode beinhaltet, realisiert. Mit diesem neuartigen Bauteil wird die Umwandlung zwischen Spin- und Ladungsströmen innerhalb der nanoskaligen Struktur untersucht. Hierbei wird die starke Spin-Bahn-Kopplung im quasi zweidimensionalen Elektronengas ausgenutzt.
Cardiovascular disease is one of the leading causes of death worldwide and, so far, echocardiography, nuclear cardiology, and catheterization are the gold standard techniques used for its detection. Cardiac magnetic resonance (CMR) can replace the invasive imaging modalities and provide a "one-stop shop" characterization of the cardiovascular system by measuring myocardial tissue structure, function and perfusion of the heart, as well as anatomy of and flow in the coronary arteries. In contrast to standard clinical magnetic resonance imaging (MRI) scanners, which are often operated at a field strength of 1.5 or 3 Tesla (T), a higher resolution and subsequent cardiac parameter quantification could potentially be achieved at ultra-high field, i.e., 7 T and above.
Unique insights into the pathophysiology of the heart are expected from ultra-high field MRI, which offers enhanced image quality in combination with novel contrast mechanisms, but suffers from spatio-temporal B0 magnetic field variations. Due to the resulting spatial misregistration and intra-voxel dephasing, these B0-field inhomogeneities generate a variety of undesired image artifacts, e.g., artificial image deformation. The resulting macroscopic field gradients lead to signal loss, because the effective transverse relaxation time T2* is shortened. This affects the accuracy of T2* measurements, which are essential for myocardial tissue characterization. When steady state free precession-based pulse sequences are employed for image acquisition, certain off-resonance frequencies cause signal voids. These banding artifacts complicate the proper marking of the myocardium and, subsequently, systematic errors in cardiac function measurements are inevitable. Clinical MR scanners are equipped with basic shim systems to correct for occurring B0-field inhomogeneities and resulting image artifacts, however, these are not sufficient for the advanced measurement techniques employed for ultra-high field MRI of the heart.
Therefore, this work focused on the development of advanced B0 shimming strategies for CMR imaging applications to correct the spatio-temporal B0 field variations present in the human heart at 7 T. A novel cardiac phase-specific shimming (CPSS) technique was set up, which featured a triggered B0 map acquisition, anatomy-matched selection of the shim-region-of-interest (SROI), and calibration-based B0 field modeling. The influence of technical limitations on the overall spherical harmonics (SH) shim was analyzed. Moreover, benefits as well as pitfalls of dynamic shimming were debated in this study. An advanced B0 shimming strategy was set up and applied in vivo, which was the first implementation of a heart-specific shimming approach in human UHF MRI at the time.
The spatial B0-field patterns which were measured in the heart throughout this study contained localized spots of strong inhomogeneities. They fluctuated over the cardiac cycle in both size and strength, and were ideally addressed using anatomy-matched SROIs. Creating a correcting magnetic field with one shim coil, however, generated eddy currents in the surrounding conducting structures and a resulting additional, unintended magnetic field. Taking these shim-to-shim interactions into account via calibration, it was demonstrated for the first time that the non-standard 3rd-order SH terms enhanced B0-field homogeneity in the human heart. However, they were attended by challenges for the shim system hardware employed in the presented work, which was indicated by the currents required to generate the optimal 3rd-order SH terms exceeding the dynamic range of the corresponding shim coils. To facilitate dynamic shimming updated over the cardiac cycle for cine imaging, the benefit of adjusting the oscillating CPSS currents was found to be vital. The first in vivo application of the novel advanced B0 shimming strategy mostly matched the simulations.
The presented technical developments are a basic requirement to quantitative and functional CMR imaging of the human heart at 7 T. They pave the way for numerous clinical studies about cardiac diseases, and continuative research on dedicated cardiac B0 shimming, e.g., adapted passive shimming and multi-coil technologies.
Strong correlations caused by interaction in systems of electrons can bring about unusual physical phenomena due to many-body quantum effects that cannot properly be captured by standard electronic structure methods like density functional theory. In this thesis, we apply the state-of-the-art continuous-time quantum Monte Carlo algorithm in hybridization expansion (CT-HYB) for the strongly correlated multi-orbital Anderson impurity model (AIM) to the solution of models of magnetic impurities on metallic surfaces and, via dynamical mean-field theory (DMFT), to the solution of a lattice model, the multi-orbital Hubbard model with Hund's coupling.
A concise introduction to the theoretical background focuses on information directly relevant to the understanding of applied models, methods, and the interpretation of results. It starts with a discussion of the AIM with its parameters and its solution in the path integral formalism, the basis of the CT-HYB algorithm. We consider its derivation and implementation in some detail before reviewing the DMFT approach to correlated lattice models and the interpretation of the single-particle Green's function.
We review two algorithmic developments for the CT-HYB algorithm that help to increase the performance of calculations especially in case of a complex structure of the interaction matrix and allow the precise calculation of self-energies and vertex functions also at intermediate and higher frequencies.
Our comparative analysis of Kondo screening in the cobalt on copper impurity system points out the importance of an accurate interaction matrix for qualitatively correct Kondo temperatures and the relevance of all d-orbitals in that case. Theoretical modeling of cobalt impurities in copper "atomic wires" fails to reproduce variations and partial absence of Kondo resonances depending on the wire size. We analyze the dependence of results on parameters and consider possible reasons for the discrepancy. Different Kondo temperatures of iron adatoms adsorbed on clean or oxygen-reconstructed niobium in the normal state are qualitatively reproduced, with the adsorption distance identified as major factor and implications for the superconducting state pointed out.
Moving on to lattice problems, we demonstrate the connection between Hund's coupling, shown to cause first-order character of the interaction-driven Mott transition at half-filling in the two-orbital Hubbard model, and a phase separation zone ending in a quantum critical point at finite doping. We touch on similarities in realistic models of iron-pnictide superconductors. We analyze the manifestation of the compressibility divergence at the finite-temperature critical points away from half-filling in the eigenbasis of the two-particle generalized susceptibility. A threshold for impurity susceptibility eigenvalues that indicates divergence of the DMFT lattice compressibility and distinguishes thermodynamic stability and instability of DMFT solutions is determined.
This thesis is aimed at establishing modalities of time-resolved photoelectron spectroscopy (tr-PES) conducted at a free-electron laser (FEL) source and at a high harmonic generation (HHG) source for imaging the motion of atoms, charge and energy at photoexcited hybrid organic/inorganic interfaces. Transfer of charge and energy across interfaces lies at the heart of surface science and device physics and involves a complex interplay between the motion of electrons and atoms. At hybrid organic/inorganic interfaces involving planar molecules, such as pentacene and copper(II)-phthalocyanine (CuPc), atomic motions in out-of-plane direction are particularly apparent. Such hybrid interfaces are of importance to, e.g., next-generation functional devices, smart catalytic surfaces and molecular machines. In this work, two hybrid interfaces – pentacene atop Ag(110) and copper(II)-phthalocyanine (CuPc) atop titanium disulfide (1T-TiSe2) – are characterized by means of modalities of tr-PES. The experiments were conducted at a HHG source and at the FEL source FLASH at Deutsches Elektronen-Synchrotron DESY (Hamburg, Germany). Both sources provide photon pulses with temporal widths of ∼ 100 fs and thus allow for resolving the non-equilibrium dynamics at hybrid interfaces involving both electronic and atomic motion on their intrinsic time scales. While the photon energy at this HHG source is limited to the UV-range, photon energies can be tuned from the UV-range to the soft x-ray-range at FLASH. With this increased energy range, not only macroscopic electronic information can be accessed from the sample’s valence and conduction states, but also site-specific structural and chemical information encoded in the core-level signatures becomes accessible. Here, the combined information from the valence band and core-level dynamics is obtained by performing time- and angle-resolved photoelectron spectroscopy (tr-ARPES) in the UV-range and subsequently performing time-resolved x-ray photoelectron spectroscopy (tr-XPS) and time-resolved photoelectron diffraction (tr-XPD) in the soft x-ray regime in the same experimental setup. The sample’s bandstructure in energy-momentum space and time is captured by a time-of-flight momentum microscope with femtosecond temporal and sub-Ångström spatial resolutions. In the investigated systems, out-of-equilibrium dynamics are traced that are connected to the transfer of charge and energy across the hybrid interfaces. While energetic shifts and complementary population dynamics are observed for molecular and substrate states, the shapes of involved molecular orbitals change in energy-momentum space on a subpicosecond time scale. In combination with theory support, these changes are attributed to iiiatomic reorganizations at the interface and transient molecular structures are reconstructed with sub-Ångström precision. Unique to the material combination of CuPc/TiSe2, a structural rearrangement on the macroscopic scale is traced simultaneously: ∼ 60 % of the molecules undergo a concerted, unidirectional in-plane rotation. This surprising observation and its origin are detailed in this thesis and connected to a particularly efficient charge transfer across the CuPc/TiSe2 interface, resulting in a charging of ∼ 45 % of CuPc molecules.
Next to the emergence of nearly isolated quantum systems such as ultracold atoms with unprecedented experimental tunability, the conceptualization of the eigenstate thermalization hypothesis (ETH) by Deutsch and Srednicki in the late 20th century has sparked exceptional interest in the mechanism of quantum thermalization. The ETH conjectures that the expectation value of a local observable within the quantum state of an isolated, interacting quantum system converges to the thermal equilibrium value at large times caused by a loss of phase coherence, referred to as dephasing. The thermal behavior within the quantum expectation value is traced back to the level of individual eigenstates, who locally act as a thermal bath to subsystems of the full quantum system and are hence locally indistinguishable to thermal states. The ETH has important implications for the understanding of the foundations of statistical mechanics, the quantum-to-classical transition, and the nature of quantum entanglement. Irrespective of its theoretical success, a rigorous proof has remained elusive so far. $$ \ $$
An alternative approach to explain thermalization of quantum states is given by the concept of typicality. Typicality deals with typical states \(\Psi\) chosen from a subspace of Hilbert space with energy \(E\) and small fluctuations \(\delta\) around it. It assumes that the possible microstates of this subspace of Hilbert space are uniformly distributed random vectors. This is inspired by the microcanonical ensemble in classical statistical mechanics, which assumes equal weights for all accessible microstates with energy \(E\) within an energy allowance \(\delta\). It follows from the ergodic hypothesis, which states that the time spent in each part of phase space is proportional to its volume leading to large time averages being equated to ensemble averages. In typicality, the Hilbert space of quantum mechanics is hence treated as an analogue of classical phase space where statistical and thermodynamic properties can be defined. Since typicality merely shifts assumptions of statistical mechanics to the quantum realm, it does not provide a complete understanding of the emergence of thermalization on a fundamental microscopic level. $$ \ $$
To gain insights on quantum thermalization and derive it from a microscopic approach, we exclusively consider the fundamental laws of quantum mechanics. In the joint work with T. Hofmann, R. Thomale and M. Greiter, on which this thesis reports, we explore the ETH in generic local Hamiltonians in a two-dimensional spin-\(1/2\) lattice with random nearest neighbor spin-spin interactions and random on-site magnetic fields. This isolated quantum system is divided into a small subsystem weakly coupled to the remaining part, which is assumed to be large and which we refer to as bath. Eigenstates of the full quantum system as well as the action of local operators on those can then be decomposed in terms of a product basis of eigenstates of the small subsystem and the bath. Central to our analysis is the fact that the coupling between the subsystem and the bath, represented in terms of the uncoupled product eigenbasis, is given by an energy dependent random band matrix, which is obtained from both analytical and numerical considerations. $$ \ $$
Utilizing the methods of Dyson-Brownian random matrix theory for random band matrices, we analytically show that the overlaps of eigenstates of the full quantum system with the uncoupled product eigenbasis are described by Cauchy-Lorentz distributions close to their respective peaks. The result is supported by an extensive numerical study using exact diagonalization, where the numerical parameters for the overlap curve agree with the theoretical calculation. The information on the decomposition of the eigenstates of the full quantum system enables us to derive the reduced density matrix within the small subsystem given the pure density matrix of a single eigenstate. We show that in the large bath limit the reduced density matrix converges to a thermal density matrix with canonical Boltzmann probabilities determined by renormalized energies of the small subsystem which are shifted from their bare values due the influence of the coupling to the bath. The behavior of the reduced density matrix is confirmed through a finite size scaling analysis of the numerical data. Within our calculation, we make use of the pivotal result, that the density of states of a local random Hamiltonian is given by a Gaussian distribution under very general circumstances. As a consequence of our analysis, the quantum expectation value of any local observable in the subsystem agrees with its thermal expectation value, which proves the validity of the ETH in the equilibrium phase for the considered class of random local Hamiltonians and elevates it from hypothesis to theory. $$ \ $$
Our analysis of quantum thermalization solely relies on the application of quantum mechanics to large systems, locality and the absence of integrability. With the self-averaging property of large random matrices, random matrix theory does not entail a statistical assumption, but is rather applied as a mathematical tool to extract information about the behavior of large quantum systems. The canonical distribution of statistical mechanics is derived without resorting to statistical assumptions such as the concepts of ergodicity or maximal entropy, nor assuming any characteristics of quantum states such as in typicality. In future research, with this microscopic approach it may become possible to exactly pinpoint the origin of failure of quantum thermalization, e.g. in systems that exhibit many body localization or many body quantum scars. The theory further enables the systematic investigation of equilibration, i.e. to study the time scales on which thermalization takes place.
The presented thesis deals with the investigation of the characteristic physical properties of lead-free double perovskites. For this purpose lead-free double perovskite single crystals were grown from solution. In order to assess the influence of growth temperature on tail states in the material, the crystals were studied using Photoluminescence Excitation (PLE) and Transmission measurements. Additionally, lead-free double perovskite solar cells and thin films were investigated to address the correlation of precursor stoichiometry and solar cell efficiency. In a last step a new earth abundant lead-free double perovskite was introduced and its physical properties were studied by photoluminescene and absorptance. Like this it was possible to assess the suitability of this material for solar cell applications in the future.
In this thesis, I establish new relations between quantum information measures in a two-dimensional CFT and geometric objects in a three-dimensional AdS space employing the AdS/CFT correspondence. I focus on two quantum information measures: the computational cost of quantum circuits in a CFT and Berry phases in two entangled CFTs. In particular, I show that these quantities are associated with geometric objects in the dual AdS space.
Topological phenomena known from solid state physics have been transferred to a variety of other classical and quantum systems. Due to the equivalence of the Hamiltonian matrix describing tight binding models and the grounded circuit Laplacian describing an electrical circuit we can investigate such phenomena in circuits. By implementing different Hermitian topological models general suggestions on designing those types of circuit are worked out with the aim of minimizing unwanted coupling effects and parasitic admittances in the circuit. Here the existence and the spatial profile of topological states as well as the band structure of the model can be determined.
Due to the complex nature of electric admittance the investigations can be directly expanded to systems with broken Hermiticity. The particular advantages of the experimental investigation of non-exclusively topological phenomena by means of electric circuits come to light in the realization of non-Hermitian and non-linear models. Here we find limitation of the Hermitian bulk-boundary correspondence principle, purely real eigenvalues in non-Hermitian PT-symmetrical systems and edge localization of all eigenstates in non-Hermitian and non-reciprocal systems, which in literature is termed the non-Hermitian skin effect.
When systems obeying non-linear equations are studied, the grounded circuit Laplacian based on the Fourier-transform cannot be applied anymore. By combination of the connectivity of a topological system together with non-linear van der Pol oscillators self-activated and self-sustained topological edge oscillations can be found. These robust high frequency sinusoidal edge oscillations differ significantly from low frequency relaxation oscillations, which can be found in the bulk of the system.
This work presents a newly developed method for the epitaxial growth of the half-Heusler antiferromagnet CuMnSb. All necessary process steps, from buffer growth to the deposition of a protective layer, are presented in detail. Using structural, electrical, and magnetic characterization, the material parameters of the epitaxial CuMnSb layers are investigated.
The successful growth of CuMnSb by molecular beam epitaxy is demonstrated on InAs (001), GaSb (001), and InP (001) substrates. While CuMnSb can be grown pseudomorphically on InAs and GaSb, the significant lattice mismatch for growth on InP leads to relaxation already at low film thicknesses. Due to the lower conductivity of GaSb compared to InAs, GaSb substrates are particularly suitable for the fabrication of CuMnSb layers for lateral electrical transport experiments. However, by growing a high-resistive ZnTe interlayer below the CuMnSb layer, lateral transport experiments on CuMnSb layers grown on InAs can also be realized. Protective layers of Ru and Al2O3 have proven to be suitable for protecting the CuMnSb layers from the environment.
Structural characterization by high resolution X-ray diffraction (full width at half maximum of 7.7 ′′ of the rocking curve) and atomic force microscopy (root mean square surface roughness of 0.14 nm) reveals an outstanding crystal quality of the epitaxial CuMnSb layers. The half-Heusler crystal structure is confirmed by scanning transmission electron microscopy and the stoichiometric material composition by Rutherford backscattering spectrometry. In line with the high crystal quality, a new minimum value of the residual resistance of CuMnSb (𝜌0 = 35 μΩ ⋅ cm) could be measured utilizing basic electrical transport experiments.
An elaborate study of epitaxial CuMnSb grown on GaSb reveals a dependence of the vertical lattice parameter on the Mn/Sb flux ratio. This characteristic enables the growth of tensile, unstrained, and compressive strained CuMnSb layers on a single substrate material. Additionally, it is shown that the Néel temperature has a maximum of 62 K at stoichiometric material composition and thus can be utilized as a selection tool for stoichiometric CuMnSb samples. Mn-related defects are believed to be the driving force for these observations.
The magnetic characterization of the epitaxial CuMnSb films is performed by superconducting quantum interference device magnetometry. Magnetic behavior comparable to the bulk material is found, however, an additional complex magnetic phase appears in thin CuMnSb films and/or at low magnetic fields, which has not been previously reported for CuMnSb. This magnetic phase is believed to be localized at the CuMnSb surface and exhibits both superparamagnetic and spin-glass-like behavior. The exchange bias effect of CuMnSb is investigated in combination with different in- and out-of-plane ferromagnets. It is shown that the exchange bias effect can only be observed in combination with in-plane ferromagnets.
Finally, the first attempts at the growth of fully epitaxial CuMnSb/NiMnSb heterostructures are presented. Both magnetic and structural studies by secondary-ion mass spectrometry indicate the interdiffusion of Cu and Ni atoms between the two half-Heusler layers, however, an exchange bias effect can be observed for the CuMnSb/NiMnSb heterostructures. Whether this exchange bias effect originates from exchange interaction between the CuMnSb and NiMnSb layers, or from ferromagnetic inclusions in the antiferromagnetic layer can not be conclusively identified.
The fact that photovoltaics is a key technology for climate-neutral energy production can be taken as a given. The question to what extent perovskite will be used for photovoltaic technologies has not yet been fully answered. From a photophysical point of view, however, it has the potential to make a useful contribution to the energy sector. However, it remains to be seen whether perovskite-based modules will be able to compete with established technologies in terms of durability and cost efficiency. The additional aspect of ionic migration poses an additional challenge. In the present work, primarily the interaction between ionic redistribution, capacitive properties and recombination dynamics was investigated. This was done using impedance spectroscopy, OCVD and IV characteristics as well as extensive numerical drift-diffusion simulations. The combination of experimental and numerical methods proved to be very fruitful. A suitable model for the description of solar cells with respect to mobile ions was introduced in chapter 4.4. The formal mathematical description of the model was transferred by a non-dimensionalization and suitable numerically solvable form. The implementation took place in the Julia language. By intelligent use of structural properties of the sparse systems of equations, automatic differentiation and the use of efficient integration methods, the simulation tool is not only remarkably fast in finding the solution, but also scales quasi-linearly with the grid resolution. The software package was released under an open source license. In conventional semiconductor diodes, capacitance measurements are often used to determine the space charge density. In the first experimental chapter 5, it is shown that although this is also possible for the ionic migration present in perovskites, it cannot be directly understood as doping related, since the space charge distribution strongly depends on the preconditions and can be manipulated by an externally applied voltage. The exact form of this behavior depends on the perovskite composition. This shows, among other things, that experimental results can only be interpreted within the framework of conventional semiconductors to a very limited extent. Nevertheless, the built-in 99 potential of the solar cell can be determined if the experiments are carried out properly. A statement concerning the type and charge of the mobile ions is not possible without further effort, while their number can be determined. The simulations were applied to experimental data in chapter 6. Thus, it could be shown that mobile ions make a significant contribution to the OCVD of perovskite solar cells. j-V characteristics and OCVD transients measured as a function of temperature and illumination intensities could be quantitatively modeled simultaneously using a single global set of parameters. By the simulations it was further possible to derive a simple experimental procedure to determine the concentration and the diffusivity of the mobile ions. The possibility of describing different experiments in a uniform temperaturedependent manner strongly supports the model of mobile ions in perovskites. In summary, this work has made an important contribution to the elucidation of ionic contributions to the (photo)electrical properties of perovskite solar cells. Established experimental techniques for conventional semiconductors have been reinterpreted with respect to ionic mass transport and new methods have been proposed to draw conclusions on the properties for ionic transport. As a result, the published simulation tools can be used for a number of further studies.
Das Ziel der vorliegenden Arbeit war die Entwicklung neuer, robuster Methoden der Spin-Lock-basierten MRT. Im Fokus stand hierbei vorerst die T1ρ-Quantifizierung des Myokards im Kleintiermodell. Neben der T1ρ-Bildgebung bietet Spin-Locking jedoch zusätzlich die Möglichkeit der Detektion ultra-schwacher, magnetischer Feldoszillationen. Die Projekte und Ergebnisse, die im Rahmen dieses Promotionsvorhabens umgesetzt und erzielt wurden, decken daher ein breites Spektrum der Spin-lock basierten Bildgebung ab und können grob in drei Bereiche unterteilt werden. Im ersten Schritt wurde die grundlegende Pulssequenz des Spin-Lock-Experimentes durch die Einführung des balancierten Spin-Locks optimiert. Der zweite Schritt war die Entwicklung einer kardialen MRT-Sequenz für die robuste Quantifizierung der myokardialen T1ρ-Relaxationszeit an einem präklinischen Hochfeld-MRT. Im letzten Schritt wurden Konzepte der robusten T1ρ-Bildgebung auf die Methodik der Felddetektion mittels Spin-Locking übertragen. Hierbei wurden erste, erfolgreiche Messungen magnetischer Oszillationen im nT-Bereich, welche lokal im untersuchten Gewebe auftreten, an einem klinischen MRT-System im menschlichen Gehirn realisiert.
Diese Arbeit befasst sich mit der Weiterentwicklung und Charakterisierung des XRM-II nanoCT Systems, sowie dessen Möglichkeiten zur Materialtrennung und Elementbestimmung in der nano-Computertomographie. Beim XRM-II nanoCT System handelt es sich um ein Röntgenmikroskop, welches in ein Rasterelektronenmikroskop integriert ist, und auf dem Prinzip der geometrischen Vergrößerung basiert. Neben zweidimensionalen Durchstrahlungsbildern ist dieses Mikroskop auch zur dreidimensionalen Bildgebung mittels Computertomographie fähig.
Der Ausgangspunkt für die Weiterentwicklung ist das XRM-II, mit welchem bereits Computertomographien im Nanometerbereich möglich waren. Deren Aufnahmedauer liegt zwischen 14 und 21 Tagen, was das System trotz seiner hohen Auflösung wenig praktikabel macht. Durch eine Anpassung der Blendeneinstellungen am Rasterelektronenmikroskop konnte der Strahlstrom um den Faktor 40 erhöht und damit die Aufnahmedauer auf 24 Stunden reduziert werden, wobei weiterhin eine zweidimensionale Auflösung von \(167 \pm 9\) nm erreicht wird. Durch die Trennung von Objekt- und Targetmanipulator lassen sich beide unabhängig und genauer bewegen, wodurch es möglich ist selbst 50 nm große Strukturen abzubilden.
Die Charakterisierung erfolgt sowohl für das komplette System als auch getrennt in die entscheidenden Komponenten wie Target und Detektor. Für das Röntgentarget werden Monte-Carlo Simulationen zur Brennfleckgröße, welche entscheidend für die erreichbare Auflösung ist, durchgeführt und mit Auflösungstests verglichen. Der Röntgendetektor wird hinsichtlich seiner spektralen Auflösung überprüft, welche hauptsächlich vom Charge Sharing Effekt beeinflusst wird. Die Charakterisierung des Gesamtsystems erfolgt durch den Vergleich mit einer höher auflösenden Bildgebungsmethode, der FIB Tomographie. Hierbei wird die gleiche Probe, ein Bruchstück einer CPU, mit beiden Methoden unter der Voraussetzung einer ähnlichen Aufnahmezeit (24 h) untersucht. In der nano-CT kann ein 12 mal größeres Volumen analysiert werden, was jedoch eine geringere räumliche Auflösung als die FIB Tomographie mit sich bringt.
Da die spektrale Auflösung des Detektors aufgrund des Charge Sharing begrenzt ist, lassen sich nur Materialien mit einem großen Unterschied in der Ordnungszahl mittels der Energieschwellen des Detektors trennen. Jedoch kann in Verbindung mit der geeigneten Wahl des Targetmaterials der Absorptionskontrast für leichte Materialien, wie beispielsweise \(SiO_2\) verbessert werden. Darüber hinaus ist es am XRM-II nanoCT möglich, durch das integrierte EDX-System, Elemente in der Computertomographie zu identifizieren. Dies wird anhand eines Drei-Wegekatalysators und eines NCA-Partikel gezeigt.
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.
Verschiedene Konzepte der Röntgenmikroskopie haben sich mittlerweile im Labor etabliert und ermöglichen heute aufschlussreiche Einblicke in eine Vielzahl von Probensystemen. Der „Labormaßstab“ bezieht sich dabei auf Analysemethoden, die in Form von einem eigenständigen Gerät betrieben werden können. Insbesondere sind sie unabhängig von der Strahlerzeugung an einer Synchrotron-Großforschungseinrichtung und einem sonst kilometergroßen Elektronen-speicherring. Viele der technischen Innovationen im Labor sind dabei ein Transfer der am Synchrotron entwickelten Techniken. Andere wiederum basieren auf der konsequenten Weiterentwicklung etablierter Konzepte. Die Auflösung allein ist dabei nicht entscheidend für die spezifische Eignung eines Mikroskopiesystems im Ganzen. Ebenfalls sollte das zur Abbildung eingesetzte Energiespektrum auf das Probensystem abgestimmt sein. Zudem muss eine Tomographieanalage zusätzlich in der Lage sein, die Abbildungsleistung bei 3D-Aufnahmen zu konservieren.
Nach einem Überblick über verschiedene Techniken der Röntgenmikroskopie konzentriert sich die vorliegende Arbeit auf quellbasierte Nano-CT in Projektionsvergrößerung als vielversprechende Technologie zur Materialanalyse. Hier können höhere Photonenenergien als bei konkurrierenden Ansätzen genutzt werden, wie sie von stärker absorbierenden Proben, z. B. mit einem hohen Anteil von Metallen, zur Untersuchung benötigt werden. Das bei einem ansonsten idealen CT-Gerät auflösungs- und leistungsbegrenzende Bauteil ist die verwendete Röntgen-quelle. Durch konstruktive Innovationen sind hier die größten Leistungssprünge zu erwarten. In diesem Zuge wird erörtert, ob die Brillanz ein geeignetes Maß ist, um die Leistungsfähigkeit von Röntgenquellen zu evaluieren, welchen Schwierigkeiten die praktische Messung unterliegt und wie das die Vergleichbarkeit der Werte beeinflusst. Anhand von Monte-Carlo-Simulationen wird gezeigt, wie die Brillanz verschiedener Konstruktionen an Röntgenquellen theoretisch bestimmt und miteinander verglichen werden kann. Dies wird am Beispiel von drei modernen Konzepten von Röntgenquellen demonstriert, welche zur Mikroskopie eingesetzt werden können. Im Weiteren beschäftigt sich diese Arbeit mit den Grenzen der Leistungsfähigkeit von Transmissionsröntgenquellen. Anhand der verzahnten Simulation einer Nanofokus-Röntgenquelle auf Basis von Monte-Carlo und FEM-Methoden wird untersucht, ob etablierte Literatur¬modelle auf die modernen Quell-konstruktionen noch anwendbar sind. Aus den Simulationen wird dann ein neuer Weg abgeleitet, wie die Leistungsgrenzen für Nanofokus-Röntgenquellen bestimmt werden können und welchen Vorteil moderne strukturierte Targets dabei bieten.
Schließlich wird die Konstruktion eines neuen Nano-CT-Gerätes im Labor-maßstab auf Basis der zuvor theoretisch besprochenen Nanofokus-Röntgenquelle und Projektionsvergrößerung gezeigt, sowie auf ihre Leistungsfähigkeit validiert. Es ist spezifisch darauf konzipiert, hochauflösende Messungen an Materialsystemen in 3D zu ermöglichen, welche mit bisherigen Methoden limitiert durch mangelnde Auflösung oder Energie nicht umsetzbar waren. Daher wird die praktische Leistung des Gerätes an realen Proben und Fragestellungen aus der Material¬wissenschaft und Halbleiterprüfung validiert. Speziell die gezeigten Messungen von Fehlern in Mikrochips aus dem Automobilbereich waren in dieser Art zuvor nicht möglich.
After the discovery of three-dimensional topological insulators (TIs), such as tetradymite chalcogenides Bi$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$ – a new class of quantum materials characterized by their unique surface electronic properties – the solid state community got focused on topological states that are driven by strong electronic correlations and magnetism. An important material class is the magnetic TI (MTI) exhibiting the quantum anomalous Hall (QAH) effect, i.e. a dissipationless quantized edge-state transport in the absence of external magnetic field, originating from the interplay between ferromagnetism and a topologically non-trivial band structure. The unprecedented opportunities offered by these new exotic materials open a new avenue for the development of low-dissipation electronics, spintronics, and quantum computation. However, the major concern with QAH effect is its extremely low onset temperature, limiting its practical application. To resolve this problem, a comprehensive understanding of the microscopic origin of the underlying ferromagnetism is necessary.
V- and Cr-doped (Bi,Sb)$_2$Te$_3$ are the two prototypical systems that have been widely studied as realizations of the QAH state. Finding microscopic differences between the strongly correlated V and Cr impurities would help finding a relevant model of ferromagnetic coupling and eventually provide better control of the QAH effect in these systems. Therefore, this thesis first focuses on the V- and Cr-doped (Bi,Sb)$_2$Te$_3$ systems, to better understand these differences. Exploiting the unique capabilities of x-ray absorption spectroscopy and magnetic circular dichroism (XAS/XMCD), combined with advanced modeling based on multiplet ligand-field theory (MLFT), we provide a detailed microscopic insight into the local electronic and magnetic properties of these systems and determine microscopic parameters crucial for the comparison with theoretical models, which include the $d$-shell filling, spin and orbital magnetic moments. We find a strongly covalent ground state, dominated by the superposition of one and two Te-ligand-hole configurations, with a negligible contribution from a purely ionic 3+ configuration. Our findings indicate the importance of the Te $5p$ states for the ferromagnetism in (Bi, Sb)$_2$Te$_3$ and favor magnetic coupling mechanisms involving $pd$-exchange. Using state-of-the-art density functional theory (DFT) calculations in combination with XMCD and resonant photoelectron spectroscopy (resPES), we reveal the important role of the $3d$ impurity states in mediating magnetic exchange coupling. Our calculations illustrate that the kind and strength of the exchange coupling varies with the impurity $3d$-shell occupation. We find a weakening of ferromagnetic properties upon the increase of doping concentration, as well as with the substitution of Bi at the Sb site. Finally, we qualitatively describe the origin of the induced magnetic moments at the Te and Sb sites in the host lattice and discuss their role in mediating a robust ferromagnetism based on a $pd$-exchange interaction scenario. Our findings reveal important clues to designing higher $T_{\text{C}}$ MTIs.
Rare-earth ions typically exhibit larger magnetic moments than transition-metal ions and thus promise the opening of a wider exchange gap in the Dirac surface states of TIs, which is favorable for the realization of the high-temperature QAH effect. Therefore, we have further focused on Eu-doped Bi$_2$Te$_3$ and scrutinized whether the conditions for formation of a substantial gap in this system are present by combining spectroscopic and bulk characterization methods with theoretical calculations. For all studied Eu doping concentrations, our atomic multiplet analysis of the $M_{4,5}$ x-ray absorption and magnetic circular dichroism spectra reveals a Eu$^{2+}$ valence, unlike most other rare earth elements, and confirms a large magnetic moment. At temperatures below 10 K, bulk magnetometry indicates the onset of antiferromagnetic ordering. This is in good agreement with DFT results, which predict AFM interactions between the Eu impurities due to the direct overlap of the impurity wave functions. Our results support the notion of antiferromagnetism coexisting with topological surface states in rare-earth doped Bi$_2$Te$_3$ and corroborate the potential of such doping to result in an antiferromagnetic TI with exotic quantum properties.
The doping with impurities introduces disorder detrimental for the QAH effect, which may be avoided in stoichiometric, well-ordered magnetic compounds. In the last part of the thesis we have investigated the recently discovered intrinsic magnetic TI (IMTI) MnBi$_6$Te$_{10}$, where we have uncovered robust ferromagnetism with $T_{\text{C}} \approx 12$ K and connected its origin to the Mn/Bi intermixing. Our measurements reveal a magnetically intact surface with a large moment, and with FM properties similar to the bulk, which makes MnBi$_6$Te$_{10}$ a promising candidate for the QAH effect at elevated temperatures. Moreover, using an advanced ab initio MLFT approach we have determined the ground-state properties of Mn and revealed a predominant contribution of the $d^5$ configuration to the ground state, resulting in a $d$-shell electron occupation $n_d = 5.31$ and a large magnetic moment, in excellent agreement with our DFT calculations and the bulk magnetometry data. Our results together with first principle calculations based on the DFT-GGA$+U$, performed by our collaborators, suggest that carefully engineered intermixing plays a crucial role in achieving a robust long-range FM order and therefore could be the key for achieving enhanced QAH effect properties.
We expect our findings to aid better understanding of MTIs, which is essential to help increasing the temperature of the QAH effect, thus facilitating the realization of low-power electronics in the future.
In der vorliegenden Arbeit werden die Konzeption und Realisierung eines Computertomographen zur Materialanalyse auf Basis eines Rasterelektronenmikroskops mit einem räumlichen Auflösungsvermögen im Nanometerbereich diskutiert. Durch einen fokussierten Elektronenstrahl, der mit einer Beschleunigungsspannung von 30 kV auf eine mikrostrukturierte Wolframnadel mit einem Spitzenradius von bis zu 50 nm gezielt wird, entsteht ein kleiner Röntgenbrennfleck über den mit geometrischer Vergrößerung hochauflösende Projektionen eines zu untersuchenden Objekts erzeugt werden. Durch Rotation des Testobjekts werden Projektionen aus verschiedenen Blickwinkeln aufgenommen und über einen speziellen Rekonstruktionsalgorithmus zu einem 3-dimensionalen Bild zusammengefügt.
Bei der Beurteilung der Einzelkomponenten des Geräts wird insbesondere auf Struktur, Form und den elektrochemischen Herstellungsprozess der Röntgenquelle eingegangen. Eine ausreichend genaue Positionierung von Messobjekt und Röntgenbrennfleck wird über Piezoachsen realisiert, während die Stabilität des Röntgenbrennflecks über die Elektronenoptik des Rasterelektronenmikroskops und die Form der Quellnadel optimiert wird.
Das räumliche Auflösungsvermögen wird über die Linienspreizfunktion an Materialkanten abgeschätzt. Für eine Wolfram-Block-Quelle ergibt sich dabei ein Auflösungsvermögen von 325 nm – 400 nm in 3D, während der Quellfleck einer Wolframnadel das Auflösungsvermögen der Anlage auf 65 nm – 90 nm in 2D und 170 nm – 300 nm in 3D bei Messungen an einem AlCu29-Testobjekt anhebt. Außerdem werden die Auswirkungen der Phasenkontrastcharakteristik der Röntgenquelle auf die rekonstruierten Bilder nach Anwendung eines Paganin-Filters diskutiert. Dabei zeigt sich, dass durch Anwendung des Filters ein verbessertes Signal-zu-Rausch-Verhältnis auf Kosten der räumlichen Bildauflösung erzielt werden kann.
Eine Vergleichsmessung mit einem kommerziell verfügbaren Röntgenmikroskop zeigt die Stärken des vorgestellten Systems bei Untersuchung von stark absorbierenden Messobjekten. Das kompakte Design erlaubt eine Weiterentwicklung in Richtung eines nanoCT-Moduls als Upgrade Option für Rasterelektronenmikroskope im Gegensatz zu den weitaus teureren bisher verbreiteten nanoCT-Geräten.
Context. In active galaxies, matter is accreted onto super massive black holes (SMBH). This accretion process causes a region roughly the size of our solar system to outshine the entire host galaxy, forming an active galactic nucleus (AGN). In some of these active galaxies, highly relativistic particle jets are formed parallel to the rotation axis of the super massive black hole. A fraction of these sources is observed under a small inclination angle between the pointing direction of the jet and the observing line of sight. These sources are called blazars. Due to the small inclination angle and the highly relativistic speeds of the particles in the jet, beaming effects occur in the radiation of these particles. Blazars can be subdivided into the high luminosity flat spectrum radio quasars (FSRQs) and the low luminosity BL Lacertae objects (BL Lacs). As all AGN, blazars are broadband emitters and therefore observable from the longest wavelengths in the radio regime to the shortest wavelengths in the gamma-ray regime. In this thesis I will analyze blazars at these two extremes with respect to their parsec-scale properties in the radio and their time evolution properties in gamma-ray flux.
Method. In the radio regime the technique of very long baseline interferometry (VLBI) can be used in order to spatially resolve the synchrotron radiation coming from those objects down to sub-parsec scales. This information can be used to observe the time evolution of the structure of such sources. This is done in large monitoring programs such as the MOJAVE (15 GHz) and the Boston University blazar monitoring program (43 GHz). In this thesis I utilize data of 28 sources from these monitoring programs spanning 10 years of observation from 2003 to 2013, resulting in over 1800 observed epochs, to study the brightness temperature and diameter gradients of these jets. I conduct a search for systematic geometry transitions in the radio jets. The synchrotron cooling time in the radio core of the jets is used to determine the magnetic field strength in the radio core. Considering the jet geometry, these magnetic field strengths are scaled to the ergosphere of the SMBH in order to obtain the distance of the radio core to the SMBH.
In the gamma-regime these blazars cannot be spatially resolved. Due to this, it is hard to put strong constrains onto where the gamma-ray emitting region is. Blazars have shown to be variable at high energies on time scales down to minutes. The nature of this variability can be studied in order to put constrains on the particle acceleration mechanism and possibly the region and size of the gamma-ray emitting region. The variability of blazars in the energy range between 0.1 GeV and 1 GeV can for example be observed with the pair-conversion telescope on board the Fermi satellite. I use 10 years of data from the Fermi-LAT (LAT: Large Area Telescope) satellite in order to study the variability of a large sample of blazars (300-800, depending on the used significance filters for data points). I quantify this variability with the Ornstein-Uhlenbeck (OU) parameters and the power spectral density (PSD) slopes. The same procedure is applied to 20 light curves available for the radio sample.
Results. The diameter evolution along the jet axis of the radio sources suggests, that FSRQs feature flatter gradients than BL Lacs. Fitting these gradients, it is revealed that BL Lacs are systematically better described by a simple single power law than FSRQs. I found 9 sources with a strongly constrained geometry transition. The sources are 0219+421, 0336-019, 0415+379, 0528+134, 0836+710, 1101+384, 1156+295, 1253-055 and 2200+420. In all of these sources, the geometry transition regions are further out in the jet than the Bondi sphere. The magnetic field strengths of BL Lacs is systematically larger than that of FSRQs. However the scaling of these fields suggest that the radio cores of BL Lac objects are closer to the SMBHs than the radio cores of FSRQs. Analyzing the variability of Fermi-LAT light curves yields consistent results for all samples. FSRQs show systematically steeper PSD slopes and feature OU parameters more favorable to strong variability than BL Lacs. The Fermi-LAT light curves of the sub-sample of radio jets, suggest an anticorrelation between the jet complexity from the radio observations and the OU-parameters as well as the PSD slopes from the gamma-ray observations.
Conclusion.
The flatter diameter gradients of FSRQs suggest that these sources are more collimated further down the jet than BL Lacs. The systematically better description of the diameter and brightness temperature gradient by a single power law of BL Lacs, suggest that FSRQs are more complex with respect to the diameter evolution along the jet and the surface brightness distribution than BL Lac objects. FSRQs often feature regions where recollimation can occur in distinct knots within the jets. For the sources where a geometry transition could be constrained, the Bondi radius, being systematically smaller than the position of the transition region along the jet axis, suggest that changing pressure gradients are not the sole cause for these systematic geometry transitions. Nevertheless they may be responsible for recollimation regions, found typically downstream the jet, beyond the Bondi radius and the transition zone. The difference in the distance of the radio cores between FSRQs and BL Lacs is most likely due to the combination of differences in SMBH masses and systematically smaller jet powers in BL Lacs. The variability in energy ranges above 100 MeV and above 1 GeV-regime suggest that many light curves of BL Lac objects are more likely to be white noise while the PSD slopes and the OU parameters of FSRQ gamma-ray light curves favor stronger variability on larger time scales with respect to the time binning of the analyzed light curve. Although the anticorrelation of the jet complexity acquired from the radio observations and the PSD slopes and OU parameters from the gamma-observations suggest that more complex sources favor OU parameters and PSD slopes resulting in more variability (not white noise) it is beyond the scope of this thesis to pinpoint whether this correlation results from causation. The question whether a complex jet causes more gamma-ray variability or more gamma-ray variability causes more complex jets cannot be answered at this point. Nevertheless the computed correlation measures suggest that this dependence is most likely not linear and therefore an indication that these effects might even interact.
This thesis addresses the identification and characterization of spin states in optoelectronic materials and devices using multiple spin-sensitive techniques. For this purpose, a systematic study focussing on triplet states as well as associated loss pathways and excited state kinetics was carried out. The research was based on comparing a range of donor:acceptor systems, reaching from organic light emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) to organic photovoltaics (OPV) employing fullerene and multiple non-fullerene acceptors (NFAs). By developing new strategies, e.g., appropriate modeling, new magnetic resonance techniques and experimental frameworks, the influence of spin states in the fundamental processes of organic semiconductors has been investigated. Thereby, the combination of techniques based on the principle of electron paramagnetic resonance (EPR), in particular transient EPR (trEPR) and optically detected magnetic resonance (ODMR), with all-optical methods, such as transient electroluminescence (trEL) and transient absorption (TA), has been employed. As a result, excited spin states, especially molecular and charge transfer (CT) states, were investigated in terms of kinetic behavior and associated pathways, which revealed a significant impact of triplet states on efficiency-limiting processes in both optoelectronic applications.
Novel appraches to the molecular beam epitaxy of core-shell nanowires in the group II telluride material system were explored in this work. Significant advances in growth spurred the development of a flexible and reliable platform for a charge transport characterization of the topological insulator HgTe in a tubular nanowire geometry. The transport results presented provide an important basis for the design of future studies that strive for the experimental realization of topological charge transport in the quantum wire limit.
The subject of this thesis is the investigation of the transport properties of topological and massive surface states in the three-dimensional topological insulator Hg(Mn)Te. These surface states give rise to a variety of extraordinary transport phenomena, making this material system of great interest for research and technological applications. In this connection, many physical properties of the topological insulator Hg(Mn)Te still require in-depth exploration. The overall aim of this thesis is to analyze the quantum transport of HgTe-based devices ranging from hundreds of micrometers (macroscopic) down to a few micrometers in size (microscopic) in order to extend the overall understanding of surface states and the possibilities of their manipulation.
In order to exploit the full potential of our high-quality heterostructures, it was necessary to revise and improve the existing lithographic fabrication process of macroscopic three-dimensional Hg(Mn)Te samples. A novel lithographic standard recipe for the fabrication of the HgTe-based macrostructures was developed. This recipe includes the use of an optimized Hall bar design and wet etching instead of etching with high-energy \(\mathrm{{Ar^{+}}}\)-ions, which can damage the samples. Further, a hafnium oxide insulator is applied replacing the SiO\(_{2}\)/Si\(_{3}\)N\(_{4}\) dielectric in order to reduce thermal load. Moreover, the devices are metallized under an alternating angle to avoid discontinuities of the metal layers over the mesa edges. It was revealed that the application of gate-dielectric and top-gate metals results in n-type doping of the devices. This phenomenon could be attributed to quasi-free electrons tunneling from the trap states, which form at the interface cap layer/insulator, through the cap into the active layer. This finding led to the development of a new procedure to characterize wafer materials. It was found that the optimized lithographic processing steps do not unintentionally react chemically with our heterostructures, thus avoiding a degradation of the quality of the Hg(Mn)Te layer. The implementation of new contact structures Ti/Au, In/Ti/Au, and Al/Ti/Au did not result in any improvement compared to the standard structure AuGe/Au. However, a novel sample recipe could be developed, resulting in an intermixing of the contact metals (AuGe and Au) and fingering of metal into the mesa. The extent of the quality of the ohmic contacts obtained through this process has yet to be fully established.
This thesis further deals with the lithographic realization of three-dimensional HgTe-based microstructures measuring only a few micrometer in size. Thus, these structures are in the order of the mean free path and the spin relaxation length of topological surface state electrons. A lithographic process was developed enabling the fabrication of nearly any desired microscopic device structure. In this context, two techniques suitable for etching microscopic samples were realized, namely wet etching and the newly established inductively coupled plasma etching. While wet etching was found to preserve the crystal quality of the active layer best, inductively coupled plasma etching is characterized by high reproducibility and excellent structural fidelity. Hence, the etching technique employed depends on the envisaged type of experiment.
Magneto-transport measurements were carried out on the macroscopic HgTe-based devices fabricated by means of improved lithographic processing with respect to the transport properties of topological and massive surface states. It was revealed that due to the low charge carrier density present in the leads to the ohmic contacts, these regions can exhibit an insulating behavior at high magnetic fields and extremely low temperatures. As soon as the filling factor of the lowest Landau levels dropped below a critical value (\(\nu_{\mathrm{{c}}}\approx0.8\)), the conductance of the leads decreased significantly. It was demonstrated that the carrier density in the leads can be increased by the growth of modulation doping layers, a back-gate-electrode, light-emitting diode illumination, and by the application of an overlapping top-gate layout. This overlapping top-gate and a back-gate made it possible to manipulate the carrier density of the surface states on both sides of the Hg(Mn)Te layer independently. With this setup, it was identified that topological and massive surface states contribute to transport simultaneously in 3D Hg(Mn)Te. A model could be developed allowing the charge carrier systems populated in the sample to be determined unambiguously. Based on this model, the process of the re-entrant quantum Hall effect observed for the first time in three-dimensional topological insulators could be explained by an interplay of n-type topological and p-type massive surface states. A well-pronounced \(\nu=-1\rightarrow\nu=-2\rightarrow\nu=-1\) sequence of quantum Hall plateaus was found in manganese-doped HgTe-based samples. It is postulated that this is the condensed-matter realization of the parity anomaly in three-dimensional topological insulators. The actual nature of this phenomenon can be the subject of further research. In addition, the measurements have shown that inter-scattering occurs between counter-propagating quantum Hall edge states. The good quantization of the Hall conductance despite this inter-scattering indicates that only the unpaired edge states determine the transport properties of the system as a whole. The underlying inter-scattering mechanism is the topic of a publication in preparation.
Furthermore, three-dimensional HgTe-based microstructures shaped like the capital letter "H" were investigated regarding spin transport phenomena. The non-local voltage signals occurring in the measurements could be attributed to a current-induced spin polarization of the topological surface states due to electrons obeying spin-momentum locking. It was shown that the strength of this non-local signal is directly connected to the magnitude of the spin polarization and can be manipulated by the applied top-gate voltage. It was found that in these microstructures, the massive surface and bulk states, unlike the topological surface states, cannot contribute to this spin-associated phenomenon. On the contrary, it was demonstrated that the population of massive states results in a reduction of the spin polarization, either due to the possible inter-scattering of massive and topological surface states or due to the addition of an unpolarized electron background. The evidence of spin transport controllable by a top-gate-electrode makes the three-dimensional material system mercury telluride a promising candidate for further research in the field of spintronics.