Localization and exact current compensation in the quantum Hall effect

TL;DR

This paper presents a field-theoretic approach to the quantum Hall effect, emphasizing the role of magnetic translation symmetry in electron localization and current compensation, which are fundamental for quantization.

Contribution

It introduces a gauge-invariant formulation demonstrating that localization and current compensation arise from magnetic translation symmetry, applicable even with level mixing and edge states.

Findings

Localization and current compensation are derived from magnetic translation symmetry.

Quantization of Hall conductance is explained through gauge invariance.

Results hold under general conditions, including level mixing and edges.

Abstract

A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of localization. It is shown, in particular, that the immobility of localized electron states and current compensation by extended electron states, both crucial for quantization of the Hall conductance, are derived through the operation of magnetic translation of localized electron states alone. They actually are consequences of gauge invariance and hold under general circumstances with both level mixing and electron edge states taken into account.