Resonant scattering in a strong magnetic field: exact density of states

TL;DR

This paper derives the exact density of states for 2D electrons in a strong magnetic field with resonant scatterers, revealing a gap formation and sensitivity to scatterer distribution, using a zero-dimensional field-theoretical approach.

Contribution

It provides an exact analytical solution for the density of states in a resonant scattering scenario, linking scattering effects to Landau level structure.

Findings

Density of states exhibits a gap under strong resonant scattering.

The Landau level shape depends critically on scatterer distribution.

Non-analytic energy dependence of the Green function is demonstrated.

Abstract

We study the structure of 2D electronic states in a strong magnetic field in the presence of a large number of resonant scatterers. For an electron in the lowest Landau level, we derive the exact density of states by mapping the problem onto a zero-dimensional field-theoretical model. We demonstrate that the interplay between resonant and non-resonant scattering leads to a non-analytic energy dependence of the electron Green function. In particular, for strong resonant scattering the density of states develops a gap in a finite energy interval. The shape of the Landau level is shown to be very sensitive to the distribution of resonant scatterers.