Floating of Extended States and Localization Transition in a Weak Magnetic Field

TL;DR

This paper numerically investigates how weak magnetic fields influence electron localization and extended states in a 2D disordered system, revealing floating extended states and critical divergence at phase boundaries.

Contribution

It demonstrates that in weak magnetic fields, extended states float up in energy and localization length diverges at phase boundaries with the same critical exponent as in high magnetic fields.

Findings

Extended states float up in energy in weak magnetic fields.

Localization length diverges at insulator phase boundary.

Critical exponent matches that of high magnetic field limit.

Abstract

We report results of a numerical study of non-interacting electrons moving in a random potential in two dimensions in the presence of a weak perpendicular magnetic field. We study the topological properties of the electronic eigenstates within a tight binding model. We find that in the weak magnetic field or strong randomness limit, extended states float up in energy. Further, the localization length is found to diverge at the insulator phase boundary with the same exponent $\nu$ as that of the isolated lowest Landau band (high magnetic field limit).