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- 2020 (13) (entfernen)
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- Englisch (13) (entfernen)
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- Kondensierte Materie (4)
- Monte-Carlo-Simulation (2)
- Supraleitung (2)
- Topologie (2)
- economic growth (2)
- energy (2)
- Active Galactic Nuclei (1)
- AdS-CFT-Korrespondenz (1)
- AdS/CFT (1)
- Centaurus A (1)
Institut
- Institut für Theoretische Physik und Astrophysik (13) (entfernen)
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.
Topological superconductors represent a fruitful playing ground for fundamental research as well as for potential applications in fault-tolerant quantum computing. Especially Josephson junctions based on topological superconductors remain intensely studied, both theoretically and experimentally. The characteristic property of these junctions is their 4-periodic ground-state fermion parity in the superconducting phase difference. Using such topological Josephson junctions, we introduce the concept of a topological Josephson heat engine. We discuss how this engine can be implemented as a Josephson-Stirling cycle in topological superconductors, thereby illustrating the potential of the intriguing and fruitful marriage between topology and coherent thermodynamics. It is shown that the Josephson-Stirling cycle constitutes a highly versatile thermodynamic machine with different modes of operation controlled by the cycle temperatures. Finally, the thermodynamic cycle reflects the hallmark 4 pi -periodicity of topological Josephson junctions and could therefore be envisioned as a complementary approach to test topological superconductivity. Topological superconductors are expected to be a key component of quantum computing systems but reliably detecting their exotic properties is a challenge. Here, the authors propose a topological Josephson heat engine which uses thermodynamic effects to probe the 4 pi -periodic ground state of a topological superconductor.
Adding interactions to topological (non-)trivial free fermion systems can in general have four different effects: (i) In symmetry protected topological band insulators, the correlations may lead to the spontaneous breaking of some protecting symmetries by long-range order that gaps the topological boundary modes. (ii) In free fermion (semi-)metal, the interaction could vice versa also generate long-range order that in turn induces a topological mass term and thus generates non-trivial phases dynamically. (iii) Correlation might reduce the topological classification of free fermion systems by allowing adiabatic deformations between states of formerly distinct phases. (iv) Interaction can generate long-range entangled topological order in states such as quantum spin liquids or fractional quantum Hall states that cannot be represented by non-interacting systems. During the course of this thesis, we use numerically exact quantum Monte Carlo algorithms to study various model systems that (potentially) represent one of the four scenarios, respectively.
First, we investigate a two-dimensional $d_{xy}$-wave, spin-singlet superconductor, which is relevant for high-$T_c$ materials such as the cuprates. This model represents nodal topological superconductors and exhibits chiral flat-band edge states that are protected by time-reversal and translational invariance. We introduce the conventional Hubbard interaction along the edge in order to study their stability with respect to correlations and find ferromagnetic order in case of repulsive interaction as well as charge-density-wave order and/or additional $i$s-wave pairing for attractive couplings. A mean-field analysis that, for the first time, is formulated in terms of the Majorana edge modes suggests that any order has normal and superconducting contributions. For example, the ferromagnetic order appears in linear superposition with triplet pairing. This finding is well confirmed by the numerically exact quantum Monte Carlo investigation.
Second, we consider spinless electrons on a two-dimensional Lieb lattice that are subject to nearest-neighbor Coulomb repulsion. The low energy modes of the free fermion part constitute a spin-$1$ Dirac cone that might be gapped by several mass terms. One option breaks time-reversal symmetry and generates a topological Chern insulator, which mainly motivated this study. We employ two flavors of quantum Monte Carlo methods and find instead the formation of charge-density-wave order that breaks particle-hole symmetry. Additionally, due to sublattices of unequal size in Lieb lattices, this induces a finite chemical potential that drives the system away from half-filling. We argue that this mechanism potentially extends the range of solvable models with finite doping by coupling the Lieb lattice to the target system of interest.
Third, we construct a system with four layers of a topological insulators and interlayer correlation that respects one independent time-reversal and a unitary $\mathbb{Z}_2$ symmetry. Previous studies claim a reduced topological classification from $\mathbb{Z}$ to $\mathbb{Z}_4$, for example by gapping out degenerate zero modes in topological defects once the correlation term is designed properly. Our interaction is chosen according to this analysis such that there should exist an adiabatic deformation between states whose topological invariant differs by $\Delta w=\pm4$ in the free fermion classification. We use a projective quantum Monte Carlo algorithm to determine the ground-state phase diagram and find a symmetry breaking regime, in addition to the non-interacting semi-metal, that separates the free fermion insulators. Frustration reduces the size of the long-range ordered region until it is replaced by a first order phase transition. Within the investigated range of parameters, there is no adiabatic path deforming the formerly distinct free fermion states into each other. We conclude that the prescribed reduction rules, which often use the bulk-boundary correspondence, are necessary but not sufficient and require a more careful investigation.
Fourth, we study conduction electron on a honeycomb lattice that form a Dirac semi-metal Kondo coupled to spin-1/2 degrees of freedom on a Kagome lattice. The local moments are described by a variant of the Balents-Fisher-Girvin model that has been shown to host a ferromagnetic phase and a $\mathbb{Z}_2$ spin liquid at strong frustration. Here, we report the first numerical exact quantum Monte Carlo simulation of the Kondo-coupled system that does not exhibit the negative-sign problem. When the local moments form a ferromagnet, the Kondo coupling induces an anti-ferromagnetic mass term in the conduction-electron system. At large frustration, the Dirac cone remains massless and the spin system forms a $\mathbb{Z}_2$ spin liquid. Owing to the odd number of spins per unit cell, this constitutes a non-Fermi liquid that violates Luttinger's theorem which relates the Fermi volume to the particle density in a Fermi liquid. This phase is a specific realization of the so called 'fractional Fermi liquid` as it has been first introduced in the context of heavy fermion models.
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.
In this review paper, we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics. We first start with the analytical properties of the classical Wright functions of which we distinguish two kinds. We then justify the relevance of the Wright functions of the second kind as fundamental solutions of the time-fractional diffusion-wave equations. Indeed, we think that this approach is the most accessible point of view for describing non-Gaussian stochastic processes and the transition from sub-diffusion processes to wave propagation. Through the sections of the text and suitable appendices, we plan to address the reader in this pathway towards the applications of the Wright functions of the second kind.
Background and Objectives
To analyze the impact of humidity and temperature on excimer laser ablation of polyethylene terephthalate (PET), polymethylmethacrylate (PMMA) and porcine corneal tissue, and an ablation model to compensate for the temperature and humidity changes on ablation efficiency.
Study Design/Materials and Methods
The study was conducted using an AMARIS 1050RS (Schwind eye‐tech‐solutions) placed inside a climate chamber at ACTS. Ablations were performed on PET, PMMA, and porcine cornea. The impact of a wide range of temperature (~18°C to ~30°C) and relative humidity (~25% to ~80%) on laser ablation outcomes was tested using nine climate test settings. For porcine eyes, change in defocus was calculated from the difference of post‐ablation to pre‐ablation average keratometry readings. Laser scanning deflectometry was performed to measure refractive change achieved in PMMA. Multiple linear regression was performed using the least square method with predictive factors: temperature, relative humidity, time stamp. Influence of climate settings was modeled for pulse energy, pulse fluence, ablation efficiency on PMMA and porcine cornea tissue.
Results
Temperature changes did not affect laser pulse energy, pulse fluence (PET), and ablation efficiency (on PMMA or porcine corneal tissue) significantly. Changes in relative humidity were critical and significantly affected laser pulse energy, high fluence and low fluence. The opposite trend was observed between the ablation performance on PMMA and porcine cornea.
Conclusions
The proposed well‐fitting multi‐linear model can be utilized for compensation of temperature and humidity changes on ablation efficiency. Based on this model, a working window for optimum operation has been found (temperature 18°C to 28°C and relative humidity 25% to 65%) for a maximum deviation of ±2.5% in ablation efficiency in PMMA and porcine corneal tissue.
The neoclassical mainstream theory of economic growth does not care about the First and the Second Law of Thermodynamics. It usually considers only capital and labor as the factors that produce the wealth of modern industrial economies. If energy is taken into account as a factor of production, its economic weight, that is its output elasticity, is assigned a meager magnitude of roughly 5 percent, according to the neoclassical cost-share theorem. Because of that, neoclassical economics has the problems of the “Solow Residual”, which is the big difference between observed and computed economic growth, and of the failure to explain the economic recessions since World War 2 by the variations of the production factors. Having recalled these problems, we point out that technological constraints on factor combinations have been overlooked in the derivation of the cost-share theorem. Biophysical analyses of economic growth that disregard this theorem and mend the neoclassical deficiencies are sketched. They show that energy’s output elasticity is much larger than its cost share and elucidate the existence of bidirectional causality between energy conversion and economic growth. This helps to understand how economic crises have been triggered and overcome by supply-side and demand-side actions. Human creativity changes the state of economic systems. We discuss the challenges to it by the risks from politics and markets in conjunction with energy sources and technologies, and by the constraints that the emissions of particles and heat from entropy production impose on industrial growth in the biosphere.
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.
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.
Although the contribution to the Isotropic Gamma-Ray Background (IGRB) from unresolved extragalactic objects has been studied for many years, its exact composition and origin are as of yet unknown. It is suspected that diffuse processes such as dark matter annihilation contribute to the total IGRB, as well as unresolved gamma-ray emission from Active Galactic Nuclei (AGN), including radio galaxies. Radio galaxies are a source class that emit strongly at radio wavelengths, some of which have also been detected at gamma-ray wavelengths by the Fermi Large Area Telescope (Fermi-LAT), and by very high energy gamma-ray Cherenkov telescopes. It is thought that due to the orientation of their jets, radio galaxies are detected less numerously at gamma-ray energies than blazars. Furthermore, only a small number of radio galaxies have been detected at gamma-ray energies though it is considered that others do as well. It is for these reasons that gamma-ray emitting radio galaxies, an interesting and elusive class of objects, are selected for investigation in this work.
In order to reach the goal of better understanding diffuse processes, it is necessary to model the radio galaxy spectral energy distributions (SEDs). As AGN emission is variable with respect to time, it is critical to use simultaneously collected observations. Calculation of the SED based on simultaneous, multiwavelength data across the electromagnetic spectrum produces a reasonably accurate representation of the state of an object in a given time range. The gamma-ray emitting radio galaxies M 87, NGC 1275, Pictor A, and Centaurus A are selected here based on having been detected in very high energy gamma-rays by Cherenkov telescopes, as well as in other wavelengths. A uniquely consistent analysis approach is applied, in which each radio galaxy is analyzed the same way using simultaneously collected data. This approach sets it apart from other studies.
Fermi-LAT raw data for each source in the sample is analyzed in time ranges which directly overlap the very high energy gamma-ray Cherenkov observations, as well as several other wavelength ranges. A synchrotron self-Compton (SSC) model is applied, which provides accurate treatment of synchrotron and inverse-Compton processes occurring in the jets of AGN, while estimating physical characteristics of the source. It is found that the spectra of M 87, NGC 1275, Pictor A, and Centaurus A can be well described by the same SSC model, producing values for the physical characteristics such as the doppler factor and magnetic field, which are relatively consistent with each other.
In order to characterize the diffuse emission from dark matter self-annihilation, the radio galaxy SEDs are also fit with a dark matter model, resulting in an estimated dark matter particle mass of around 4.7 TeV which lies within predicted ranges.
The highly dense regions near the black holes of AGN provide the optimal conditions for detecting these signatures. It is also found here that discrepancies between the expected emission and the observed emission in the spectra of some radio galaxies can be explained using the combined SSC and dark matter model. As emission from dark matter annihilation is expected to remain steady with respect to time, a key feature of this work is the novelty of the combined SSC and dark matter model, and the finding that dark matter characteristics may be revealed through similar multiwavelength analyses during future low emission states of the AGN.
The radio galaxy sample is then extended to include all gamma-ray emitting radio galaxies detected by the Fermi-LAT, and a calculation of the core radio, total radio, and gamma-ray luminosities is followed through. A future step in extending this work would be to estimate the gamma-ray luminosity function of radio galaxies and their percent contribution to the total IGRB, based on the widely agreed upon assumption that a reasonable estimate of the gamma-ray luminosity function of a population can be attained by appropriately scaling its radio luminosity function, as gamma-ray luminosities and radio luminosities are strongly linearly correlated. This work has also provided the basis for such a calculation by outlining the theory and initial steps.
It is the hope that the vast scope of the gathered data, its simultaneity, and the use of consistent analysis methods across the sample, will provide an improved foundation for a future calculation of the contribution of this population to the IGRB, as well as encourage stricter requirements for multiwavelength studies.