Weak Field Phase Diagram for an Integer Quantum Hall Liquid

TL;DR

This study investigates the localization and phase diagram of an integer quantum Hall liquid at weak magnetic fields, revealing a linear relationship of extended state energy with magnetic field and the existence of a critical magnetic field below which extended states vanish.

Contribution

It provides a new phase diagram for the weak field quantum Hall regime, highlighting the linear dependence of extended state energies and the critical magnetic field for localization.

Findings

Extended state energy $E_c$ is always linear in magnetic field.

Existence of a critical magnetic field $B_c$ below which extended states disappear.

Lower Landau levels are more robust with smaller $B_c$.

Abstract

We study the localization properties in the transition from a two-dimensional electron gas at zero magnetic field into an integer quantum Hall (QH) liquid. By carrying out a direct calculation of the localization length for a finite size sample using a transfer matrix technique, we systematically investigate the field and disorder dependences of the metal-insulator transition in the weak field QH regime. We obtain a different phase diagram from the one conjectured in previous theoretical studies. In particular, we find that: (1) the extended state energy $E_{c}$ for each Landau level (LL) is {\it always} linear in magnetic field; (2) for a given Landau level and disorder configuration there exists a critical magnetic field $B_{c}$ below which the extended state disappears; (3) the lower LLs are more robust to the metal-insulator transition with smaller $B_{c}$. We attribute the above results to strong LL coupling effect. Experimental implications of our work are discussed.