Theory of exciton-electron scattering in atomically thin semiconductors

Christian Fey,Peter Schmelcher,Richard Schmidt,Atac Imamoglu

doi:10.1103/physrevb.101.195417

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.

Highlights

The realization of mixtures of excitons and charge carriers in van der Waals materials presents a 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
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

Summary

INTRODUCTION

Interacting mixtures of fermions and bosons are at the heart of many paradigms of condensed matter physics, ranging from phonon and magnon-mediated superconductivity, mixtures of helium-3 and helium-4, polaron mobility, to electrons coupled to dynamical gauge fields. With transition metal dichalcogenides a new class of atomically thin semiconductors with potential technological applications has emerged [24] that provides a novel platform to realize strongly interacting mixtures of pointlike bosons and fermions. In contrast to their bulk counterparts, in atomically thin materials screening of Coulomb forces is reduced owing to the absence of an all-encompassing dielectric environment. Our approach gives access to the structure of three-body envelope wave functions as well as scattering states above the trion dissociation threshold From this we show that the picture of exciton-electron scattering and the description in terms of Bose-Fermi mixtures is well justified.

EFFECTIVE MASS MODEL

ELECTRON-EXCITON SCATTERING

OPTICAL ABSORPTION SPECTRUM OF