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The bipolariton model and the concept of excitonic-biexcitonic mixed modes in semiconductors

An alternative approach to the so called bipolariton concept has been proposed. We have shown that the bipolariton approximation can indeed be used for calculating the elementary excitation spectrum in the photon-exciton-biexciton system in its biexciton part. The bipolariton concept does not provide the correct spectrum in the excitonic-polariton energy part, where the existence of four-particle electron-hole bound states should be considered. In order to go beyond the bipolariton approximation we developed a Green function formalism for the theory of an interacting electron-photon system in which photons, excitons and biexcitons are treated on an equal level. Our approach is a completely microscopic treatment and is based on the assumption that the excitons and biexcitons are two- and four-particle bound states, formed by electrons and holes. The method of Legendre transforms is used to derive a set of nine independent exact equations for the corresponding vertex and Green functions. Knowledge of the solutions of the above equations provide the excitation energies of the quasiparticles (excitonic-biexcitonic polaritons) formed by coupling of photons with excitons and biexcitons. Those elementary excitations manifest themselves as common poles of the photon propagator, two- and four-particle electron-hole Green functions.