Anti-Levitation in the Integer Quantum Hall Systems

TL;DR

This paper numerically investigates the behavior of extended states in the integer quantum Hall regime, revealing an anti-levitation phenomenon where extended states move below Landau energies with increasing disorder or decreasing magnetic field.

Contribution

It introduces the concept of anti-levitation of extended states in the integer quantum Hall system through numerical simulations, highlighting the effects of disorder and magnetic field.

Findings

Extended states move below Landau energies with increased disorder or decreased magnetic field.

Existence of a disorder-dependent critical magnetic field below which no extended states exist.

A phase diagram delineating localized and delocalized states in the W-1/B plane.

Abstract

Two-dimensional electron gas in the integer quantum Hall regime is investigated numerically by studying the dynamics of an electron hopping on a square lattice subject to a perpendicular magnetic field and random on-site energy with white noise distribution. Focusing on the lowest Landau band we establish an anti-levitation scenario of the extended states: As either the disorder strength $W$ increases or the magnetic field strength $B$ decreases, the energies of the extended states move below the Landau energies pertaining to a clean system. Moreover, for strong enough disorder, there is a disorder dependent critical magnetic field $B_c(W)$ below which there are no extended states at all. A general phase diagram in the $W-1/B$ plane is suggested with a line separating domains of localized and delocalized states.