Hall conductivity as a topological invariant

TL;DR

This paper investigates the quantum Hall effect by examining its topological properties and symmetries, focusing on a two-dimensional electron system under electric and magnetic fields, and explores Hall conductivity quantization beyond linear response.

Contribution

It introduces analysis of Hall conductivity quantization in a two-dimensional lattice model beyond the linear response regime, emphasizing topological invariants.

Findings

Hall conductivity quantization extends beyond linear response

Topological invariants characterize the quantum Hall effect

Symmetry considerations elucidate the Hall effect mechanisms

Abstract

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 and perpendicular magnetic field. We refer to this as the two dimensional electric-magnetic Bloch problem (EMB). The Hall conductivity quatizations beyond the linear response approximation is analyzed.