Electronic structure and absorption spectrum of biexciton obtained by using exciton basis

TL;DR

This paper develops a novel approach to solving the biexciton Schrödinger equation using an exciton basis and composite boson formalism, and applies it to calculate optical absorption spectra in quantum wells.

Contribution

It introduces a new method for analyzing biexcitons via exciton basis and composite boson formalism, providing insights into their energy states and optical properties.

Findings

Biexciton ground-state energy aligns with variational results.

Identified optical absorption features related to biexciton states.

Calculated absorption spectra showing characteristic peaks and tails.

Abstract

We approach the biexciton Schr\"{o}dinger equation not through the free-carrier basis as usually done, but through the free-exciton basis, exciton-exciton interactions being treated according to the recently developed composite boson many-body formalism which allows an exact handling of carrier exchange between excitons, as induced by the Pauli exclusion principle. We numerically solve the resulting biexciton Schr\"{o}dinger equation with the exciton levels restricted to the ground state and we derive the biexciton ground state as well as the bound and unbound excited states as a function of hole-to-electron mass ratio. The biexciton ground-state energy we find, agrees reasonably well with variational results. Next, we use the obtained biexciton wave functions to calculate optical absorption in the presence of a dilute exciton gas in quantum well. We find a small asymmetric peak with a characteristic low-energy tail, identified with the biexciton ground state, and a set of large peaks associated with biexciton unbound states, i.e., exciton-exciton scattering states.