Physical principles underlying the quantum Hall effect

TL;DR

This paper introduces the physical principles of the quantum Hall effect, emphasizing the field theoretic approach, gauge anomaly cancellation, and applications to interference experiments.

Contribution

It provides a comprehensive overview of the underlying physics and formalism of the quantum Hall effect, including edge state mechanisms and experimental interpretations.

Findings

Edge states cancel gauge anomalies

Formalism aids in interference experiment design

Insights into fractional and integral quantum Hall effects

Abstract

In this contribution, we present an introduction to the physical principles underlying the quantum Hall effect. The field theoretic approach to the integral and fractional effect is sketched, with some emphasis on the mechanism of electromagnetic gauge anomaly cancellation by chiral degrees of freedom living on the edge of the sample. Applications of this formalism to the design and theoretical interpretation of interference experiments are outlined.