Harmonic Solid Theory of Photoluminescence in the High Field Two-Dimensional Wigner Crystal

TL;DR

This paper models the photoluminescence spectrum of a high-field two-dimensional Wigner crystal using harmonic solid theory, successfully reproducing experimental line shapes and analyzing disorder effects.

Contribution

It introduces a harmonic solid model combined with time-dependent perturbation theory to describe photoluminescence in 2D Wigner crystals, providing insights into spectral line shapes and disorder influences.

Findings

Spectral line shapes match experimental observations

Disorder models affect spectral width predictions

The model suggests mechanisms for improved quantitative agreement

Abstract

Motivated by recent experiments on radiative recombination of two-dimensional electrons in acceptor doped GaAs-AlGaAs heterojunctions as well as the success of a harmonic solid model in describing tunneling between two-dimensional electron systems, we calculate within the harmonic approximation and the time dependent perturbation theory the line shape of the photoluminescence spectrum corresponding to the recombination of an electron with a hole bound to an acceptor atom. The recombination process is modeled as a sudden perturbation of the Hamiltonian for the in-plane degrees of freedom of the electron. We include in the perturbation, in addition to changes in the equilibrium positions of electrons, changes in the curvatures of the harmonically approximated potential. The computed spectra have line shapes similar to that seen in a recent experiment. The spectral width, however, is roughly a factor of 3 smaller than that seen in experiment if one assumes a perfect Wigner crystal for the initial state state of the system, whereas a simple random disorder model yields a width a factor of 3 too large. We speculate on the possible mechanisms that may lead to better quantitative agreement with experiment.