相关论文: Topological quantum numbers in the Hall effect

Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the Z index of topological…

Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant…

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over…

The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and…

We discuss a model for the integer quantum Hall effect which is based on a Schroedinger-Chern-Simons-action functional for a non-interacting system of electrons in an electromagnetic field on a mutiply connected manifold. In this model the…

The quantum Hall effect is one of the most extensively studied topological effects in solid state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous…

An effective action for the bulk dynamics of quantum Hall effect in arbitrary even spatial dimensions was obtained some time ago in terms of a Chern-Simons term associated with the Dolbeault index theorem. Here we explore further properties…

A square lattice model which exhibits a nonzero quantized Hall conductance in a zero net magnetic field at certain values of the parameters is presented. The quantization is due to the existence of a topological winding number that…

Quantum anomalous Hall (QAH) insulators are two-dimensional (2D) insulating states exhibiting properties similar to those of quantum Hall states but without external magnetic field. They have quantized Hall conductance $\sigma^H=Ce^2/h$,…

Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…

We study transport properties and topological phase transition in two-dimensional interacting disordered systems. Within dynamical mean-field theory, we derive the Hall conductance, which is quantized and serves as a topological invariant…

The fundamental collective degree of freedom of fractional quantum Hall states is identified as a unimodular two-dimensional spatial metric that characterizes the local shape of the correlations of the incompressible fluid. Its quantum…

It is widely accepted that topological quantities are useful to describe quantum liquids in low dimensions. The (spin) Hall conductances are typical examples. They are expressed by the Chern numbers, which are topological invariants given…

The quantized thermal Hall effect is an important probe for detecting chiral topological order and revealing the nature of chiral gapless edge states. The standard Kubo formula approach for the thermal Hall conductance $\kappa_{xy}$ based…

Topology plays a central role in nearly all disciplines of physics, yet its applications have so far been restricted to closed, lossless systems in thermodynamic equilibrium. Given that many physical systems are open and may include gain…

Studying deterministic operators, we define an appropriate topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer…

We give an overview of the Integer Quantum Hall Effect. We propose a mathematical framework using Non-Commutative Geometry as defined by A. Connes. Within this framework, it is proved that the Hall conductivity is quantized and that…

We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically,…

The experimental observation of the long-sought quantum anomalous Hall effect was recently reported in magnetically doped topological insulator thin films [Chang et al., Science 340, 167 (2013)]. An intriguing observation is a rapid…

The object of the present work is to study the quantum Hall effect through its symmetries and topological aspects. We consider the model of an electron moving in a two-dimensional lattice in the presence of applied in-plain electric field…