Lift of degeneracy of Landau levels of 2D electron gas by point-like impurities

TL;DR

This paper demonstrates that point-like impurities in a 2D electron gas under magnetic field lift Landau level degeneracy, revealing a density of states inversely proportional to energy offset, applicable across various 2D systems.

Contribution

It shows that impurity scattering fully lifts Landau level degeneracy, contradicting previous unphysical models, and characterizes the resulting density of states behavior.

Findings

Degeneracy of Landau levels is completely lifted by impurities.

Density of states near Landau levels is inversely proportional to energy offset.

Results are relevant for multiple 2D electron systems.

Abstract

We study the density of states of two-dimensional electron gas in magnetic field with scattering on point-like impurities that are uniformly distributed along the sample. We show that the electron-impurity interaction completely lifts the degeneracy of the Landau levels even at low impurity concentration. This statement is in contradiction with the previous results obtained in the unphysical approximation of two-dimensional impurities. There is a large region of the electron energy $\omega $, counted from the Landau level, where the density of states $\rho (\omega)$ is inversely proportional to $|\omega|$ and proportional to the impurity concentration. Our results are applicable to different 2D electron systems as heterostructures, inversion layers and interfaces.