Exact Quantum Virial Expansion for the Optical Response of Doped Two-Dimensional Semiconductors

TL;DR

This paper develops an exact quantum virial expansion for the optical response of doped 2D semiconductors, accurately predicting features like exciton-electron scattering effects and unifying different theoretical models.

Contribution

It introduces a perturbatively exact virial expansion applicable in high-temperature or low-doping regimes, unifying trion and Fermi polaron theories for 2D semiconductors.

Findings

Excellent agreement with recent experiments on doped monolayer MoSe2

Reveals the non-trivial shape of the attractive branch in photoluminescence

Suggests previous measurements overestimated trion binding energy

Abstract

We present a quantum virial expansion for the optical response of a doped two-dimensional semiconductor. As we show, this constitutes a perturbatively exact theory in the high-temperature or low-doping regime, where the electrons' thermal wavelength is smaller than their interparticle spacing. The virial expansion predicts new features of the photoluminescence, such as a non-trivial shape of the attractive branch related to universal low-energy exciton-electron scattering and an associated shift of the attractive peak from the trion energy. Our results are in excellent agreement with recent experiments on doped monolayer MoSe$_2$ [Zipfel et al., Phys. Rev. B 105, 075311 (2022)] and they imply that the trion binding energy is likely to have been overestimated in previous measurements. Our theory furthermore allows us to formally unify two distinct theoretical pictures that have been applied to this system, with the conventional trion picture results emerging as a high-temperature and weak-interaction limit of Fermi polaron theory.