Γ-X mixing in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As coupled double quantum wells under hydrostatic pressure

We have investigated the energies of the electronic states of GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As strongly coupled double quantum wells and uncoupled multiple quantum wells as functions of hydrostatic pressure up to 35 kbar. The energies of the quantum-well states at 4 K were determined at each pressure by photoluminescence excitation spectra. The pressure coefficients of the energies of the allowed transitions between the valence-band and conduction-band quantized states of wide (200 Å) uncoupled wells were all equal to the pressure coefficient of the bulk GaAs band gap. For a strongly coupled double quantum well consisting of two 72-Å wells separated by an 18-Å barrier, the energies of the allowed transitions all showed a decrease in their pressure coefficients beginning near 20 kbar. These results are interpreted in terms of a drop in the conduction-band quantum-well confinement energy, due to Γ-X mixing, as the X valleys of the barrier materials are brought nearly equal to the energies of the confined electron states by pressure. An envelope-function-approximation model which includes Γ-X mixing at the interfaces is compared quantitatively with these results and found to be consistent for a certain range of the phenomenological mixing strength of the model.