Metal-insulator transition in a multilayer system with a strong magnetic field

TL;DR

This paper investigates the Anderson localization and phase transitions in a multilayer system under a strong magnetic field, revealing a phase diagram with quantum Hall, metallic, and insulating phases, and determining the critical exponent of localization.

Contribution

It provides the phase diagram and critical exponent for localization in a multilayer system with magnetic field and disorder, highlighting the existence of a quantum Hall phase.

Findings

Quantum Hall phase exists at weak disorder

Mobility edge separates insulating and metallic phases at intermediate disorder

All states localized at high disorder, leading to an insulating phase

Abstract

We study the Anderson localization in a weakly coupled multilayer system with a strong magnetic field perpendicular to the layers. The phase diagram of 1/3 flux quanta per plaquette is obtained. The phase diagram shows that a three-dimensional quantum Hall effect phase exists for a weak on-site disorder. For intermediate disorder, the system has insulating and normal metallic phases separated by a mobility edge. At an even larger disorder, all states are localized and the system is an insulator. The critical exponent of the localization length is found to be $\nu=1.57\pm0.10$.