Splitting of the Landau levels by magnetic perturbations and Anderson transition in 2D-random magnetic media

TL;DR

This paper investigates how random magnetic perturbations affect Landau levels in 2D systems, demonstrating the coexistence of localized and delocalized states and providing explicit examples of spectral splitting.

Contribution

It proves the existence of localized and delocalized states in a Landau Hamiltonian with random magnetic perturbations and constructs explicit magnetic perturbations causing Landau level splitting.

Findings

Localized states at spectrum edges

Delocalized states near band centers

Explicit magnetic perturbations splitting Landau levels

Abstract

In this note we consider a Landau Hamiltonian perturbed by a random magnetic potential of Anderson type. For a given number of bands, we prove the existence of both strongly localized states at the edges of the spectrum and dynamical delocalization near the center of the bands in the sense that wave packets travel at least at a given minimum speed. We provide explicit examples of magnetic perturbations that split the Landau levels into full intervals of spectrum.