Landau Level Mixing and Levitation of Extended States in Two Dimensions

TL;DR

This paper investigates how mixing Landau levels affects the energies of extended states in a 2D system under strong magnetic fields, revealing an upward shift proportional to the Landau level index and inverse cube of the magnetic field.

Contribution

It introduces a systematic perturbative approach to quantify Landau level mixing effects on extended state energies in two dimensions.

Findings

Extended states shift upward due to Landau level mixing.

Levitation magnitude scales as (n+1/2)/B^3 for strong magnetic fields.

The approach provides a quantitative framework for understanding Landau level interactions.

Abstract

We study the effects of mixing of different Landau levels on the energies of one-body states, in the presence of a strong uniform magnetic field and a random potential in two dimensions. We use a perturbative approach and develop a systematic expansion in both the strength and smoothness of the random potential. We find the energies of the extended states shift {\em upward}, and the amount of levitation is proportional to $(n+1/2)/B^3$ for strong magnetic field, where $B$ is the magnetic field strength and $n$ is the Landau level index.