Theory of Exciton Recombination from the Magnetically Induced Wigner Crystal

TL;DR

This paper develops a theoretical framework for understanding how exciton recombination spectra are affected by the presence of a magnetically induced Wigner crystal in two-dimensional electron systems, highlighting the role of electron-hole separation.

Contribution

It introduces a detailed theory linking exciton recombination features to the structure and correlations of the magnetically induced Wigner crystal, accounting for varying electron-hole separation.

Findings

Additional spectral peaks appear for small electron-hole separation due to reciprocal lattice vectors.

Spectral structure reflects short-range correlations when separation exceeds magnetic length.

Derived expressions for energies and radiative lifetimes of exciton states.

Abstract

We study the theory of itinerant-hole photoluminescence of two-dimensional electron systems in the regime of the magnetically induced Wigner crystal. We show that the exciton recombination transition develops structure related to the presence of the Wigner crystal. The form of this structure depends strongly on the separation $d$ between the photo-excited hole and the plane of the two-dimensional electron gas. When $d$ is small compared to the magnetic length, additional peaks appear in the spectrum due to the recombination of exciton states with wavevectors equal to the reciprocal lattice vectors of the crystal. For $d$ larger than the magnetic length, the exciton becomes strongly confined to an interstitial site of the lattice, and the structure in the spectrum reflects the short-range correlations of the Wigner crystal. We derive expressions for the energies and the radiative lifetimes of the states contributing to photoluminescence, and discuss how the results of our analysis compare with experimental observations.