Inversion asymmetry, hole mixing, and enhanced Pockels effect in quantum wells and superlattices

The effects of inversion asymmetry on the anisotropic optical transition in the presence of electric field (Pockels effect) in GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells and superlattices are investigated theoretically. Within an 8×8 k⋅p effective mass Hamiltonian formalism, in which the linear k, ${\mathit{k}}^3$, ε (strain due to the piezoelectric effect), εk, and Rashba terms are taken into account, we have derived the renormalized effective Hamiltonian for the electron and hole, respectively. The effects of the inversion asymmetry and the hole mixing on the spin-split subband structures and the dependence of optical transition matrix elements on the polarization of incident light are fully presented. The microscopic model clearly shows that the inversion asymmetry is responsible for the Pockels effect. The roles played by the hole mixing in the enhanced quantum well Pockels effect mediated by the electron-hole pairs are shown by our calculations. Thus, we develop a theory with exciton states with eight spin components (due to the broken twofold degeneracy of the electrons) in the quantum well and calculate the excitonic spectra. The symmetry analysis and numerical results indicate that the excitonic anisotropic behavior results from the interference between different spin components of holes, which, owing to the heavy- and light-hole mixing, is enhanced significantly compared with the bulk material, especially for those exciton states whose dominant component does not coincide with its optically active component. Comparison between theory and experiment is discussed.