Splitting of Landau levels of a 2D electron due to electron-phonon interactions

TL;DR

This paper demonstrates that strong magnetic fields cause electron-phonon interactions to split 2D electron Landau levels into infinitely degenerate sublevels, with energy spacing decreasing as magnetic field strength increases.

Contribution

It provides a detailed qualitative and quantitative analysis of Landau level splitting due to electron-phonon interactions in high magnetic fields, considering acoustic and optical phonons.

Findings

Landau levels split into infinitely degenerate sublevels under strong magnetic fields.

Energy spacing between sublevels decreases as B^{-1/2} at large B.

Both acoustic and optical phonon interactions cause similar splitting behavior.

Abstract

We show that in a very strong magnetic field $B$ electron-phonon interaction gives rise to a splitting of Landau levels of a 2D electron into a series of infinitely degenerate sublevels. We provide both qualitative and quantitative description of this phenomenon. The cases of interaction with acoustic and polar optical phonons are considered. The energy distance between nearest sublevels in both cases tends to zero as $B^{-1/2}$ at large $B$.