Related papers: Disordered Topological Insulators: A Non-Commutati…
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…
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…
The pumping conductance of a disordered two-dimensional Chern insulator scales with increasing size and fixed disorder strength to sharp plateau transitions at well-defined energies between ordinary and quantum Hall insulators. When the…
Topological insulators (TIs) are a new quantum state of matter discovered recently, which are characterized by unconventional bulk topological invariants. Proposals for practical applications of the TIs are mostly based upon their metallic…
The appearance of fractional Chern insulators in moir\'e systems can be rationalized by the presence of a fictitious magnetic field associated with the spatial texture of layer-resolved electronic wavefunctions. Here, we present a…
We develop a topological theory for disordered Weyl semimetals in the framework of gauge invariance of replica formalism and boundary-bulk correspondence of Chern insulators. An anisotropic topological $\theta$-term is analytically derived…
A quantum anomalous Hall state with high Chern number has so far been realized in multiplayer structures consisting of alternating magnetic and undoped topological insulator layers. However, in previous proposals, the Chern number can be…
We study the nu=1/3 quantum Hall state in presence of the random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to unambiguously distinguish between insulating and current…
In this work, we propose the average spin Chern number (ASCN) as an indicator of the topological significance of the spin degree of freedom within insulating materials. Whenever this number is a non-zero even integer, it distinguishes the…
One of the main topological invariants that characterizes several topologically-ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in…
The effect of strong disorder on chiral-symmetric 3-dimensional lattice models is investigated via analytical and numerical methods. The phase diagrams of the models are computed using the non-commutative winding number, as functions of…
In this work we consider whether nonsymmorphic symmetries such as a glide plane can protect the existence of topological crystalline insulators and superconductors in three dimensions. In analogy to time-reversal symmetric insulators, we…
In two-dimensional topological insulators, a disorder induced topological phase transition is typically identified with an Anderson localization transition at the Fermi energy. However, in higher-order, spin-resolved topological insulators…
Commonly, a two-dimensional topological insulator is characterized by non-zero Chern numbers associated with its band structure. In our work, we present the experimental demonstration of an anomalous topological insulator, for which the…
Of the available classes of insulators which have been shown to contain topologically non-trivial properties one of the most important is class AII, which contains systems that possess time-reversal symmetry $T$ with $T^2=-1.$ This class…
The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the…
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 investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the…
Topological insulators are characterized by specially protected conduction on their outer boundaries. We show that the protected edge conduction exhibited by 2-D topological insulators (and also Chern insulators) is independent of…
The low-energy physics of two-dimensional Quantum Anomalous Hall insulators like (Hg,Mn)Te quantum wells or magnetically doped (Bi,Sb)Te thin films can be effectively described by two Chern insulators, including a Dirac, as well as a…