The Mesoscopic Quantum-Hall-Insulator Transition

TL;DR

This paper investigates the localization transitions in disordered quantum wires under strong magnetic fields, revealing sharp conductance transitions and complex phase diagrams influenced by electron spin effects.

Contribution

It introduces a new understanding of the mesoscopic quantum Hall-insulator transition driven by dimensional crossovers and spin effects, with detailed phase diagram analysis.

Findings

Conductance exhibits sharp, discontinuous transitions at zero temperature.

Phase diagram includes multiple phases influenced by Zeeman energy.

Plateau widths depend on spin flip rate.

Abstract

Sharp localization transitions of chiral edge states in disordered quantum wires, subject to strong magnetic field, are shown to be driven by crossovers from two- to one-dimensional localization of bulk states. As a result, the two-terminal conductance is found to exhibit at zero temperature discontinuous transitions between {\it exactly} integer plateau values and zero, reminiscent of first order phase transitions. We discuss the corresponding phase diagram. The spin of the electrons is shown to result in a multitude of phases, when the spin degeneracy is lifted by the Zeeman energy. The width of conductance plateaus is found to depend sensitively on the spin flip rate $1/\tau_s$.