Related papers: Three-Band Model for Quantum Hall and Spin Hall Ef…
The celebrated Shastry Sutherland model has a gapped dimer singlet ground state. The material SrCu$_2$(BO$_3$)$_2$ serves as a good realization of this model, upto small anisotropies arising from Dzyaloshinskii-Moriya (DM) interactions. The…
We study the XX model for quantum spins on the star graph with three legs (i.e., on a Y-junction). By performing a Jordan-Wigner transformation supplemented by the introduction of an auxiliary space we find a Kondo Hamiltonian of fermions,…
We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are…
We investigate topological Hall effects in a metallic antiferromagnetic (AFM) thin film and/or at the interface of an AFM insulator-normal metal bilayer with a single skyrmion in the diffusive regime. To determine the spin and charge Hall…
We propose an approach based on the generalized quantum mechanics to deal with the basic features of the spin Hall effect. We begin by considering two decoupled harmonic oscillators on the noncommutative plane and determine the solutions of…
The review is aimed at highlighting the aspects of topological superconductivity in the absence of spin-orbit interaction in two-dimensional systems with long-range non-collinear spin ordering or magnetic skyrmions. Another purpose is to…
Motivated by the observation of topological states in AB-stacked MoTe$_2$/WSe$_2$, we construct the symmetry-adapted Wannier states and tight-binding model for the quantum spin Hall bands in this system. Our construction is based on the…
We study the vanishing of the topological properties of a quantum spin Hall insulator induced by a deformation of the band structure that interpolates between the Dirac and the semi-Dirac limits of a tight-binding model on a honeycomb…
A knot theory for two-dimensional square lattice is proposed, which sheds light on design of new two-dimensional material with high topological numbers. We consider a two-band model, focusing on the Hall conductance {\sigma}xy = e^2/hbar*P,…
The redistribution of energy levels between energy bands is studied for a family of simple effective Hamiltonians depending on one control parameter and possessing axial symmetry and energy-reflection symmetry. Further study is made on the…
The higher-order corner modes for quantum anomalous Hall insulators in $C_3$ symmetry broken honeycomb lattice have been engineered recently. Here we consider an extended Haldane model in presence of inversion symmetry breaking sub-lattice…
Topology can manifest topological magnetism (e.g., skyrmion and bimeron) in real space and quantum anomalous Hall (QAH) state in momentum space, which have changed the modern conceptions of matter phase. While the topologies in different…
The title material has a quasi-one-dimensional electronic structure and is of considerable interest because it has a metallic phase with properties different from a simple Fermi liquid, a poorly understood "insulating" phase, and a…
We present a comprehensive theoretical study of the topological properties of triplon excitations in spin-1/2 dimer-singlet ground states defined on the maple leaf and star lattices. Our analysis is based on a model that includes Heisenberg…
The general solution of SUSY intertwining relations for three-dimensional Schr\"odinger operators is built using the class of second order supercharges with nondegenerate constant metric. This solution includes several models with arbitrary…
Based on the standard many-fermion field theory, the authors construct models describing ultracold fermions in a 1D optical lattices by implementing a mode expansion of the fermionic field operator where modes, in addition to space…
We establish a connection between an arbitrary Hermitian tight-binding model with chiral (C) symmetry and its non-Hermitian counterpart with chiral-time (CT ) symmetry.We show that such a non-Hermitian Hamiltonian is pseudo-Hermitian. The…
Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low…
In this paper, we present a novel experimental approach for simulating and detecting topological invariants using ultracold fermions confined in two-dimensional hexagonal optical lattices. We propose achieving two-fold degenerate four-band…
A method for deriving superintegrable Hamiltonians with a spin orbital interaction is presented. The method is applied to obtain a new superintegrable system in Euclidean space $\mathbb{E}_3$ with the following properties. It describes a…