Turning many-body problems to few-body ones in photoexcited semiconductors using the stochastic variational method in momentum space, SVM-k

TL;DR

This paper introduces an efficient stochastic variational method in momentum space for calculating complex excitonic states in photoexcited semiconductors, accounting for many-body interactions and exchange effects.

Contribution

The authors develop a novel computational approach that simplifies the many-body problem into a few-body one using the stochastic variational method in momentum space.

Findings

Analytical expressions for potential matrix elements derived.

Method effectively captures electron-hole and exchange interactions.

Provides detailed insights into particle energies and distributions.

Abstract

We develop an efficient computational technique to calculate composite excitonic states in photoexcited semiconductors through the stochastic variational method (SVM). Many-body interactions between an electron gas and the excitonic state are embodied in the problem through Fermi holes in the conduction band, introduced when electrons are pulled out of the Fermi sea to bind the photoexcited electron-hole pair. We consider the direct Coulomb interaction between distinguishable particles in the complex, the exchange-induced band-gap renormalization effect, and electron-hole exchange interaction between an electron and its conduction-band hole. We provide analytical expressions for potential matrix elements, using a technique that allows us to circumvent the difficulty imposed by the occupation of low-energy electron states in the conduction band. We discuss the computational steps one should implement in order to perform the calculation, and how to extract kinetic energies of individual particles in the complex, average inter-particle distances, and density distributions.