Theory of exciton-electron scattering in atomically thin semiconductors

TL;DR

This paper develops an exact diagonalization method to analyze exciton-electron interactions in atomically thin semiconductors, providing insights into bound states, scattering, and many-body effects relevant for optoelectronic applications.

Contribution

It introduces a novel diagonalization approach for three-body problems in 2D semiconductors, enabling accurate predictions of scattering and bound states for excitons and electrons.

Findings

Accurately predicts exciton and trion energies matching Quantum Monte Carlo results.

Derives an effective exciton-electron scattering potential for many-body theories.

Demonstrates impact of finite-range corrections on optical spectra.

Abstract

The realization of mixtures of excitons and charge carriers in van-der-Waals materials presents a new frontier for the study of the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy model for such systems, we develop an exact diagonalization approach based on a discrete variable representation that predicts the scattering and bound state properties of three charges in two-dimensional transition metal dichalcogenides. From the solution of the quantum mechanical three-body problem we thus obtain the bound state energies of excitons and trions within an effective mass model which are in excellent agreement with Quantum Monte Carlo predictions. The diagonalization approach also gives access to excited states of the three-body system. This allows us to predict the scattering phase shifts of electrons and excitons that serve as input for a low-energy theory of interacting mixtures of excitons and charge carriers at finite density. To this end we derive an effective exciton-electron scattering potential that is directly applicable for Quantum Monte-Carlo or diagrammatic many-body techniques. As an example, we demonstrate the approach by studying the many-body physics of exciton Fermi polarons in transition-metal dichalcogenides, and we show that finite-range corrections have a substantial impact on the optical absorption spectrum. Our approach can be applied to a plethora of many-body phenomena realizable in atomically thin semiconductors ranging from exciton localization to induced superconductivity.