Theory of polariton-electron interactions in semiconductor microcavities

TL;DR

This paper provides a microscopic theory of polariton-electron interactions in semiconductor microcavities, revealing enhanced scattering effects and resonance phenomena beyond simple approximations, with implications for various material systems.

Contribution

It introduces an exact microscopic calculation of polariton-electron interactions, surpassing the Born approximation, and uncovers resonance effects influenced by light-matter coupling.

Findings

Polariton-electron scattering can be significantly stronger than exciton-electron scattering.

The Born approximation overestimates the interaction strength at zero momentum.

A resonance-like peak in scattering occurs near the polariton inflection point.

Abstract

We develop a microscopic description of an electron-doped two-dimensional semiconductor embedded in a microcavity. Specifically, we investigate the interactions between exciton-polaritons and electrons for the case where the interactions between charges are strongly screened and the system is spin polarized. As a starting point, we obtain an analytic expression for the exciton-polariton wave function, and we relate the microscopic parameters of the light-matter system to experimentally measurable quantities, such as the Rabi coupling and the cavity photon frequency. We then derive the polariton-electron interaction within the standard Born approximation and compare it with the exact polariton-electron scattering $T$ matrix that we obtain from a diagrammatic approach that has proven highly successful in the context of nuclear physics and ultracold atomic gases. In particular, we show that the Born approximation provides an upper bound on the polariton-electron coupling strength at vanishing momentum. Using our exact microscopic calculation, we demonstrate that polariton-electron scattering can be strongly enhanced compared to the exciton-electron case, which is the opposite of that expected from the Born approximation. We furthermore expose a resonance-like peak at scattering momenta near the polariton inflection point, whose size is set by the strength of the light-matter coupling. Our results arise from the non-Galilean nature of the polariton system and should thus be applicable to a range of semiconductor microcavities such as GaAs quantum wells and atomically thin materials.