Coulomb Interaction in Atomically Thin Semiconductors and Density-Independent Exciton-Scattering Processes

TL;DR

This paper develops a detailed quantum-kinetic framework for Coulomb interactions in atomically thin semiconductors, emphasizing many-body correlations, screening effects, and scattering processes relevant for exciton dynamics.

Contribution

It introduces a second-quantized Coulomb Hamiltonian in a Heisenberg approach, linking ab initio screening methods with effective-mass models for exciton scattering.

Findings

Derived a second-quantized Coulomb Hamiltonian for 2D semiconductors.

Analyzed Umklapp processes and local-field effects in dielectric screening.

Clarified Coulomb scattering processes affecting exciton energies.

Abstract

In quantum-kinetic approaches to the dynamics of Coulomb-bound many-body correlations such as excitons, trions, biexcitons or higher-order correlations, a detailed knowledge of the many-body Coulomb Hamiltonian serving as a starting point is important. In this manuscript, the second-quantized description of the Coulomb interaction between Bloch electrons in a Heisenberg-equation-of-motion approach in atomically thin semiconductors is derived and reviewed. Emphasis is put on a discussion of Umklapp processes and the dielectric screening including all local-field effects. A link between \textit{ab initio} methods of screening and few-band models in effective-mass approximations for the quantum kinetics is established and all important Coulomb scattering processes contributing to the exciton energy landscape and density-independent exciton scattering are discussed.