On the effect of far impurities on the density of states of two-dimensional electron gas in a strong magnetic field

TL;DR

This paper investigates how impurities at various distances from a 2D electron gas influence its density of states in a strong magnetic field, revealing significant differences from in-plane impurity models.

Contribution

It provides an exact calculation of the density of states considering impurities at different distances, extending previous models to more realistic impurity distributions.

Findings

Density of states differs qualitatively with impurity distance

Small impurity concentration leads to distinct density of states behavior

Impurity placement significantly affects electronic properties in magnetic fields

Abstract

The effect of impurities situated at different distances from a two-dimensional electron gas on the density of states in a strong magnetic field is analyzed. Based on the exact result of Brezin, Gross, and Itzykson, we calculate the density of states in the whole energy range, assuming the Poisson distribution of impurities in the bulk. It is shown that in the case of small impurity concentration the density of states is qualitatively different from the model case when all impurities are located in the plane of the two-dimensional electron gas.