Electron Localization in the Quantum-Hall Regime

TL;DR

This paper explores how electron localization explains both the insulating behavior and the quantization of transverse conductivity in quantum-Hall systems, linking fundamental electronic properties.

Contribution

It demonstrates that electron localization underpins both the vanishing longitudinal conductivity and the quantized transverse conductivity in quantum-Hall fluids.

Findings

Localization tensor is finite in insulators, divergent in metals.

Off-diagonal imaginary part of the tensor relates to transverse conductivity.

Electron localization causes both conductivity suppression and quantization.

Abstract

The theory of the insulating state discriminates between insulators and metals by means of a localization tensor, which is finite in insulators and divergent in metals. In absence of time-reversal symmetry, this same tensor acquires an offdiagonal imaginary part, proportional to the dc transverse conductivity, leading to quantization of the latter in two-dimensional systems. I provide evidence that electron localization--in the above sense--is the common cause for both vanishing of the dc longitudinal conductivity and quantization of the transverse one in quantum-Hall fluids.