Solution of the X-ray edge problem for 2D electrons in a magnetic field

TL;DR

This paper analytically calculates the absorption and emission spectra of transitions involving a localized level and a 2D electron gas in a weak magnetic field, revealing spectral line intensities and their relation to Fermi edge singularity.

Contribution

It provides an exact analytical expression for spectral line intensities using Landau level bosonization, extending understanding of the X-ray edge problem in magnetic fields.

Findings

Exact spectral line intensity expressions derived

Envelope function resembles Fermi edge singularity

Results recover known behavior in zero magnetic field limit

Abstract

The absorption and emission spectra of transitions between a localized level and a two-dimensional electron gas, subjected to a weak magnetic field, are calculated analytically. Adopting the Landau level bosonization technique developed in previous papers, we find an exact expression for the relative intensities of spectral lines. Their envelope function, governed by the interaction between the electron gas and the core hole, is reminescent of the famous Fermi edge singularity, which is recovered in the limit of a vanishing magnetic field.