Related papers: The 6D quantum Hall effect and 3D topological pump…
Controllability of ultracold atomic gases has reached an unprecedented level, allowing for experimental realization of the long-sought-after Thouless pump, which can be interpreted as a dynamical quantum Hall effect. On the other hand, Weyl…
Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and…
This review deals with strongly disordered topological insulators and covers some recent applications of a well established analytic theory based on the methods of Non-Commutative Geometry (NCG) and developed for the Integer Quantum…
We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized…
Two-dimensional 2-bands insulators breaking time reversal symmetry can present topological phases indexed by a topological invariant called the Chern number. Here we first propose an efficient procedure to determine this topological index.…
Three-dimensional (3D) topological materials exhibit much richer phenomena than their lower-dimensional counterparts. Here, we propose self-localized topological states (i.e., topological solitons) in a 3D nonlinear photonic Chern…
We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standard properties of Laughlin theory, such as the…
Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show…
Based on a quasi-one-dimensional limit of quantum Hall states on a thin torus, we construct a model of interaction-induced topological pumping which mimics the Hall response of the bosonic integer quantum Hall (BIQH) state. The…
The study of topological property of band insulators is an interesting branch of condensed matter physics. Two types of topologically nontrivial insulators have been extensively studied. The first type is characterized by a nonzero TKNN…
Motivated by the recent experimental realization of the half-quantized Hall effect phase in a three-dimensional (3D) semi-magnetic topological insulator [M. Mogi et al., Nature Physics 18, 390 (2022)], we propose a scheme for realizing the…
We introduce a simple method to realize and detect photonic topological Chern insulators with one-dimensional circiut quantum electrodynamics arrays. By periodically modulating the couplings of the array, we show that this one-dimensional…
Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. The integer quantum Hall effect has delivered…
Chern insulator or quantum anomalous Hall state is a topological state with integer Hall conductivity but in absence of Landau level. It had been well established on various two-dimensional lattices with periodic structure. Here, we report…
Considerable efforts have recently been devoted to the experimental realization of a two-dimensional Chern insulator, i.e., a system displaying a quantum anomalous Hall effect. However, existing approaches such as those based on magnetic…
We perform a detail study of higher dimensional quantum Hall effects and A-class topological insulators with emphasis on their relations to non-commutative geometry. There are two different formulations of non-commutative geometry for…
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials…
Using a well known singular gauge transformation, certain fractional quantized Hall states can be modeled as integer quantized Hall states of transformed fermions interacting with a Chern-Simons field. In previous work we have calculated…
We investigate topological states of two-dimensional (2D) triangular lattices with multi-orbitals. Tight-binding model calculations of a 2D triangular lattice based on $\emph{p}_{x}$ and \emph{p}_{y} orbitals exhibit very interesting doubly…
We consider a generalization of the 2-dimensional (2D) quantum-Hall insulator to a non-compact, non-Abelian gauge group, the Heisenberg-Weyl group. We show that this kind of insulator is actually a layered 3D insulator with nontrivial…