Momentum-space solution of exciton excited states and heavy-hole–light-hole mixing in quantum wells

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Abstract
A full valence-band mixing model for excitons in quantum wells is presented. The exciton equation is solved in momentum space using the modified Gaussian quadrature method, taking into account the angular dependence of the excitons. The theory accounts for the mixing of the ground state of the light-hole exciton and the excited states of the heavy-hole exciton at low temperatures reported previously by Viña et al. [Phys. Rev. Lett. 58, 832 (1987)]. Our calculations reproduce correctly the resonant field, the minimum energy split at the resonant field, and the fine structure of the competing 2s and 2p states resolved in the experimental data. For the s-states-dominated spectra, the full model can be simplified to include only s-states coupling. We show that the numerical results based on the simplified model match very well the polarization-dependent room-temperature exciton absorption spectra of Miller et al. [IEEE J. Quantum Electron. QE-22, 1816 (1986)].