Phase diagram of localization in a magnetic field

TL;DR

This paper numerically maps the phase diagram of localization in a 3D disordered system under a magnetic field, revealing how the magnetic field influences the transition between localized and delocalized states.

Contribution

It provides a detailed numerical analysis of the localization phase diagram in a magnetic field, confirming power law behavior and showing field-induced localization effects.

Findings

Mobility edge shifts with magnetic field

Localized states near phase boundary become delocalized

Magnetic field causes localization of extended states near band tail

Abstract

The phase diagram of localization is numerically calculated for a three-dimensional disordered system in the presence of a magnetic field using the Peierls substitution. The mobility edge trajectory shifts in the energy-disorder space when increasing the field. In the band center, localized states near the phase boundary become delocalized. The obtained field dependence of the critical disorder is in agreement with a power law behavior expected from scaling theory. Close to the tail of the band the magnetic field causes localization of extended states.