Theory of Phonon Shakeup Effects on Photoluminescence from the Wigner Crystal in a Strong Magnetic Field

TL;DR

This paper presents a quantum-mechanical method to analyze phonon shakeup effects on photoluminescence in a 2D Wigner crystal under strong magnetic fields, distinguishing it from liquid states and exploring electron-hole interactions.

Contribution

It introduces a non-harmonic, collective mode-based approach to compute shakeup effects, advancing understanding of crystal versus liquid states in magnetic fields.

Findings

Shakeup produces identifiable sidebands in the spectrum.

Crystal and liquid states show different shakeup behaviors.

Lattice relaxation causes a shift in the main luminescence peak.

Abstract

We develop a method to compute shakeup effects on photoluminescence from a strong magnetic field induced two-dimensional Wigner crystal. Only localized holes are considered. Our method treats the lattice electrons and the tunneling electron on an equal footing, and uses a quantum-mechanical calculation of the collective modes that does not depend in any way on a harmonic approximation. We find that shakeup produces a series of sidebands that may be identified with maxima in the collective mode density of states, and definitively distinguishes the crystal state from a liquid state in the absence of electron-hole interaction. In the presence of electron-hole interaction, sidebands also appear in the liquid state coming from short-range density fluctuations around the hole. However, the sidebands in the liquid state and the crystal state have different qualitative behaviors. We also find a shift in the main luminescence peak, that is associated with lattice relaxation in the vicinity of a vacancy. The relationship of the shakeup spectrum with previous mean-field calculations is discussed.