Localization in the quantum Hall regime

TL;DR

This paper reviews the localization properties of electron states in the quantum Hall regime, discussing various models, critical behaviors, and the interplay between edge states and bulk localization, highlighting the universal aspects and phase transitions.

Contribution

It introduces and compares multiple theoretical models for localization in the quantum Hall regime and discusses the critical behavior and edge-bulk interplay in finite systems.

Findings

Universal critical behavior of localization length summarized

Predicted breakdown of two-point conductance in finite systems

Interplay between edge states and bulk localization analyzed

Abstract

The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced. Descriptions in terms of equivalent tight-binding Hamiltonians, and the 2D Dirac model, are outlined. Evidences for the universal critical behavior of the localization length are summarized. A short review of the supersymmetric critical field theory is provided. The interplay between edge states and bulk localization properties is investigated. For a system with finite width and with short-range randomness, a sudden breakdown of the two-point conductance from $ne^{2}/h$ to 0 ($n$ integer) is predicted if the localization length exceeds the distance between the edges.