Topological Excitations and Anomalous Transport Phenomena in Condensed Matter Systems

Topological physics is a burgeoning new area of study in condensed matter systems, focusing on the topological excitations as well as the transport phenomena of systems with topologically non-trivial band structures. These systems being either gapped or gapless, are topologically protected and can support new phenomena which are absent in topologically trivial systems. The gapless topological superconductors can host Majorana zero modes, known as the interpretation of the Majorana fermions in condensed matter systems, which have been proposed as the ideal qubit for topological quantum computation due to their non-Abelian topological properties. The gapped topological insulators, on the other hand, can realize the non-dissipation transport charge and spin currents, which are immune to defects and directly related to the topologically non-trivial Berry curvature of the Bloch bands of the electrons. In this thesis, we will discuss the topological features of topological superconductors, higher-order superfluids, and topological insulators. For the studies on topological superconductors, we focus on investigating the properties of Majorana fermions using numerical modeling as well as theoretical methods. We also elucidate the formation of the so-called quasi-Majoranas or partially separated Andreev bound states in semiconductor superconductor heterostructures, and discuss the feasibility of braiding in the quasi-Majorana regime. Using ultra-cold atoms in optical lattices, we propose a Hofstadter-Hubbard model to realize the higher-order topological superfluid capable of supporting the Majorana corner modes, which are degenerate and protected by time-reversal symmetry. In the aspect of the anomalous transport phenomena manifested by the Berry phase effect, we propose the non-linear anomalous Nernst effect and the non-linear anomalous thermal Hall effect in time-reversal invariant systems. By analyzing the anomalous transport coefficients, we also propose the analog of the Wiedemann-Franz law and Mott formula for the non-linear transport phenomena

Wiedemann-Franz law and Mott relation for non-linear anomalous transport phenomena

Berry curvature dipole has been shown to produce non-linear anomalous Hall effect which is non-zero even in the presence of time-reversal symmetry. In this paper, within the framework of semiclassical Boltzmann theory, we calculate the analytical expressions for the non-linear anomalous transport coefficients, namely, the non-linear anomalous Hall, Nernst, and thermal Hall coefficients. With these expressions, we predict the fundamental relations between the non-linear anomalous electric and thermo-electric transport coefficients, which are the analog of the Wiedemann-Franz law and the Mott relation in the non-linear regime. We also make experimental predictions for anomalous thermal Hall coefficient for monolayer transition metal dichalcogenide which can be verified in experiments.Comment: 10 pages, 4 figure

Coupling of quantum-dot states via elastic-cotunneling and crossed Andreev reflection in a minimal Kitaev chain

Recently, exciting progress has been made in using the superconducting nanowires coupled to gate-defined quantum dots (QDs) to mimic the Kiteav chain and realize the Majorana-bound states via a poor man's route. The essential ingredient is to balance the interdot elastic-cotunneling (ECT) and crossed Andreev reflection (CAR). As theoretically proposed, this can be mediated by the Andreev bound states (ABSs) formed in the superconducting nanowires. However, most of the gate-tuning asymmetric features observed in experiments can not be captured using the current theoretical models. To address this insufficiency, here, we consider a full model that explicitly includes all the details of both the QD states and the ABSs. Remarkable agreement is found with the recent experimental observations, where our model correctly reveals the gate-tuning asymmetry in ECTs and by which the average QD state energy can also be extracted. In contrast, CARs do not depend on the tuning of QD states. Moreover, armed with the tunability of ECTs and CARs with QD states, we also predict a controllable anisotropic superexchange interaction between electron spins in the two separated QDs

Partially-separated Majorana modes in a disordered medium

Focusing on the implications of recent experiments on Majorana zero modes in semiconductor-superconductor (SM-SC) heterostructures, we critically examine the quantization of the zero-bias differential conductance as a possible unambiguous signature of Majorana physics in the presence of disorder. By numerically calculating the zero-bias conductance (ZBC) maps as function of Zeeman splitting and chemical potential for different disorder realizations, we show that the presence of quantized "islands" characterized by a ZBC value (approximately) equal to $2e^2/h$ and having a finite area/volume in a multi-dimensional parameter space represents a unique signature of Majorana physics supporting Majorana zero modes (MZMs) or partially-separated Majorana modes (ps-MMs). We find that in the presence of strong disorder Majorana physics only emerges locally and gives rise to ps-MMs, which, in turn, generate small quantized islands when one of the Majorana modes is located at the end of the system. Observing these small islands may require sample selection and the systematic scanning of a large volume in the control parameter space. Upon decreasing disorder, the quantized islands increase in size and eventually coalesce into large topological regions. Since the presence of MZMs localized at the opposite ends of the system is typically associated with large quantized islands, looking for MZM-induced edge-to-edge correlations is premature in the absence of convincing experimental evidence for (even small) quantized islands. We conclude that the observation of quantized islands demonstrates unambiguously the presence of the key ingredients necessary for Majorana physics, provides an excellent diagnostic tool for evaluating the disorder strength, and, consequently, represents the next natural milestone in the Majorana search.Comment: 12 pages, 10 figures. Published versio

Third-order Hall effect in the surface states of a topological insulator

Time reversal and inversion symmetric materials fail to yield linear and nonlinear responses since they possess net zero Berry curvature. However, higher-order Hall response can be generated in these systems upon constraining the crystalline symmetries. Motivated by the recently discovered third-order Hall (TOH) response mediated by Berry connection polarizability, namely, the variation the Berry connection with respect to an applied electric field, here we investigate the existence of such Hall effect in the surface states of hexagonal warped topological insulator (e.g., Bi$_2$Te$_3$) under the application of electric field only. Using the semiclassical Boltzmann formalism, we investigate the effect of tilt and hexagonal warping on the Berry connection polarizability tensor and consequently, the TOH effect provided the Dirac cone remains gapless. We find that the magnitude of the response increases significantly with increasing the tilt strength and warping and therefore, they can provide the tunability of this effect. In addition, we also explore the effect of chemical doping on TOH response in this system. Interestingly, we show based on the symmetry analysis, that the TOH can be the leading-order response in this system which can directly be verified in experiments.Comment: 9 pages, 2 figure