Exact shape of the lowest Landau level in a double--layer system and a superlattice with uncorrelated disorder

TL;DR

This paper extends Wegner's exact solution for the lowest Landau level density of states to double-layer systems and superlattices with uncorrelated disorder, revealing how disorder affects miniband structure and Landau level broadening.

Contribution

It provides an analytical expression for double-layer systems and an integral equation for superlattices, advancing understanding of disorder effects on Landau levels.

Findings

Analytical density of states for double-layer systems.

Numerical analysis of miniband disappearance with increasing disorder.

Insight into the interplay between tunneling and disorder broadening.

Abstract

We extend Wegner's exact solution for the 2D density of states at the lowest Landau level with a short--range disorder to the cases of a double--layer system and a superlattice. For the double--layer system, an analytical expression for the density of states, illustrating the interplay between the tunnel splitting of Landau levels and the disorder--induced broadening, is obtained. For the superlattice, we derive an integral equation, the eigenvalue of which determines the exact density of states. By solving this equation numerically, we trace the disappearance of the miniband with increasing disorder.