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

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

1996-08-15

arxiv.org/abs/cond-mat/9608066v1

Phys. Rev. Lett. 77, 5106 (1996)

Physics

Condensed Matter

12 pages + 3 figures

Scientific paper

10.1103/PhysRevLett.77.5106

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.

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