Related papers: Tunable quantum metric and band topology in bilaye…
We construct quasi one-dimensional topological and non-topological three-band lattices with tunable band gap and winding number of the flat band. Using mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we…
We develop a unified quantum geometric framework to understand reactive quantum dynamics. The critical roles of the quantum geometry of adiabatic electronic states in both adiabatic and non-adiabatic quantum dynamics are unveiled. A…
Topology plays an important role in non-hermitian systems. How to characterize a non-hermitian topological system under open-boundary conditions(OBCs) is a challenging problem. A one-dimensional(1D) topological invariant defined on a…
The newly discovered topological crystalline insulators (TCIs) harbor a complex band structure involving multiple Dirac cones. These materials are potentially highly tunable by external electric field, temperature or strain and could find…
Designer 2D materials where the constituent layers are not aligned may result in band structures with dispersionless, "flat" bands. Twisted bilayer graphene has been found to show correlated phases as well as superconductivity related to…
This thesis explores the application of differential geometric and general relativistic techniques to deepen our understanding of quantum mechanical systems. We focus on three systems, employing these mathematical frameworks to uncover…
Topological physics has broadened its scope from the study of topological insulating phases to include nodal phases containing band structure singularities. The geometry of the corresponding quantum states is described by the quantum metric…
Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…
Topological edge states in Chern insulators are typically characterized by a linear dispersion relation inherited from the Dirac structure of the bulk Hamiltonian. Here we show that this paradigm can be fundamentally altered in systems with…
The magnetic field dependence of energy levels in gapped single- and bilayer graphene quantum dots (QDs) defined by electrostatic gates is studied analytically in terms of the Dirac equation. Due to the absence of sharp edges in these types…
Dirac materials are of great interest as condensed matter realizations of the Dirac and Weyl equations. In particular, they serve as a starting point for the study of topological phases. This physics has been extensively studied in…
We develop a theoretical framework for designing quantum couplers based on Dirac materials that can modulate the polarization of transmitted quasiparticles without significantly perturbing their propagation. We analyze in detail the…
The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three dimensional analogues of graphene, in which the Dirac nodes are protected by…
We make a spectral analysis of the massive Dirac operator in a tubular neighborhood of an unbounded planar curve,subject to infinite mass boundary conditions. Under general assumptions on the curvature, we locate the essential spectrum and…
The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but…
Quantum geometry provides important information about the structure and topology of quantum states in various forms of quantum matter. The information contained therein has profound effects on observable quantities such as superconducting…
Topological phases of materials are characterized by topological invariants that are conventionally calculated by different means according to the dimension and symmetry class of the system. For topological materials described by Dirac…
We have investigated the interplay between band inversion and size quantization in spherically shaped nanoparticles made from topological-insulator (TI) materials. A general theoretical framework is developed based on a versatile…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
Topological insulators (TIs) are an important family of quantum materials that exhibit a Dirac point (DP) in the surface band structure but have a finite band gap in bulk. A large degree of spin-orbit interaction and low bandgap is a…