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

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.

12 pages + 3 figures

References in corpus (1)

• Three-dimensional disordered conductors in a strong magnetic field: surface states and quantum Hall plateaus

Cited by in corpus (4)

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• Resonant scattering in a strong magnetic field: exact density of states
• Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry
• Exact shape of the lowest Landau level in a spin-1/2 system with uncorrelated disorders