Delocalization of electrons in a Random Magnetic Field

TL;DR

This paper investigates how a random magnetic field affects electron localization in a 2D system, revealing a phase transition from insulator to metal characterized by quantized Hall conductance and energy-dependent localization.

Contribution

It demonstrates the existence of a metal-insulator transition in a 2D electron system under a random magnetic field, with critical energies and exponents depending on field strength.

Findings

Extended states exhibit quantized Hall conductance.

A metal-insulator phase transition occurs at critical energies.

Localization length and critical energies depend on magnetic field strength.

Abstract

Delocalization problem for a two-dimensional non-interacting electron system is studied under a random magnetic field. With the presence of a random magnetic field, the Hall conductance carried by each eigenstate can become nonzero and quantized in units of $e^2/h$. Extended states are characterized by nonzero Hall conductance, and by studying finite-size scaling of the density of extended states, an insulator-metal phase transition is revealed. The metallic phase is found at the center of energy band which is separated from the localized states at the band tails by critical energies $\pm E_c$. Both localization exponent and the critical energy $E_c$ are shown to be dependent on the strength of random magnetic field.