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

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.