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

•New composite boson many-body theory is used to derive exactly the biexciton Schrödinger equation using the exciton basis.•We solved the 2D and 3D biexciton ground- and excited-state binding energies for various electron-to-hole mass ratios.•The absorption spectrum shows an asymmetric low-energy peak identified with the biexciton ground state.•High-energy Lorentzian-like peaks in the absorption spectrum are associated with the exciton–exciton scattering states.•The exciton gas momentum distribution can be determined by the absorption spectrum via the biexciton wave functions.

We approach the biexciton Schrödinger 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 Schrödinger 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 an asymmetric peak with a characteristic low-energy tail, identified with the biexciton ground state, and a set of Lorentzian-like peaks associated with biexciton unbound states, i.e., exciton–exciton scattering states. Last, we propose a pump–probe experiment to probe the momentum distribution of the exciton condensate.