On the gauge invariant and topological nature of the localization determining the Quantum Hall Effect plateaus

TL;DR

This paper explores how the electromagnetic response in the Quantum Hall Effect regime, characterized by topological Chern-Simons theory, explains the stabilization of Hall plateaus through impurity charge reservoirs, emphasizing gauge invariance and topological aspects.

Contribution

It provides a gauge-invariant, topological framework linking the electromagnetic response to localization and plateau formation in the Quantum Hall Effect.

Findings

Impurities act as charge reservoirs stabilizing Hall plateaus.

Chern-Simons theory describes the topological electromagnetic response.

Analytical realization of electron motion along equipotential lines.

Abstract

It is shown how the electromagnetic response of the 2DEG under Quantumm Hall Effect regime, chracterized by the Chern-Simons topological action, transforms the sample impurities and defects in charge reservoirs that stabilize the the Hall conductivity plateaus. The results, determine the basic dynamical origin of the singular properties of localization under the occurrence of the QHE obtained in the pioneering works of Laughlin and of Joynt and Prange, by means of a gauge invariance argument and a purely electronic analysis, respectively. The common picture of electrons moving the equipotential lines gets an analytical realization through the Chern-Simons current and charge densities.