Exciton polaritons and hyper-Raman scattering in zinc-blende-type semiconductors: CuBr as an example

Abstract

The dispersion of excitons and hence of excitonic polaritons in zinc-blende-type semiconductors reflects the complexity of the band structure of these materials. We calculate the dispersion of the exciton branches ${E}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}})$ of the eightfold ground state from an invariant expansion of the center-of-mass Hamiltonian, including exchange interaction, up to second order in the exciton total wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$. The excitonic polaritons are then constructed according to Hopfield's polariton theory, which is extended to the case of more than one oscillator. The polariton dispersion is experimentally studied for CuBr by hyper-Raman scattering via biexcitons. The selection rules for this process are calculated for different scattering configurations, whereby the symmetry of the biexciton ground state, having components of ${\ensuremath{\Gamma}}_{1}$, ${\ensuremath{\Gamma}}_{3}$, and ${\ensuremath{\Gamma}}_{5}$ symmetry, is considered. A self-consistent analysis of the observed hyper-Raman emission lines yields the dispersion of the multicomponent excitonic polaritons in CuBr.