Exact shape of the lowest Landau level in a spin-1/2 system with uncorrelated disorders

TL;DR

This paper derives an analytical expression for the density of states of a spin-1/2 disordered 2D electron gas in a strong magnetic field, revealing how disorder and Zeeman splitting influence Landau level broadening and splitting.

Contribution

It provides the first analytical formula for the density of states considering spin and disorder effects in a 2D electron system under strong magnetic fields.

Findings

Disorder enhances Landau level broadening and splitting.

Level repulsion from spin mixing increases band broadening.

Comparison with double-layer systems highlights spin effects.

Abstract

Using the path-integral approach developed by Br\'ezin et al. [ Nucl.Phys.B235, 24 (1984) ], we obtain an analytical expression for the density of states of a spin-1/2 disordered two-dimensional electron gas in a strong, perpendicular magnetic field. The density of states of this system illustrates the interplay between the Zeeman splitting of Landau levels and the disorder-induced broadening. We find that the broadening and the band splitting of the Landau bands are enhanced due to the level repulsion from the mixing of two spin orientations caused by the random scatterings. The comparison between the spin-1/2 model and the double-layer system is also discussed.