ANALYTIC SOLUTIONS FOR THE VALENCE SUBBAND MIXING AT THE ZONE CENTER OF A GAAS ALXGA1-XAS QUANTUM-WELL UNDER UNIAXIAL-STRESS PERPENDICULAR TO THE GROWTH DIRECTION/

Using the envelope-function approach, we present a theoretical analysi s of the effects of uniaxial stress applied along the [100] direction on the zone-center valence stares of a type-I GaAs/GaxAl1-xAs [001] qu antum well. The resulting strain reduces the symmetry and causes mixin g between heavy and light holes which can be described approximately w ithin the Gamma(8) subspace by a 4x4 Luttinger-Kohn Hamiltonian in con junction with the correct 4x4 Bir-Pikus strain Hamiltonian. An approxi mate analytic solution is found by expanding the finite-stress solutio ns in terms of the zero-stress eigenstates. This representation allows a detailed analysis of the strain-induced coupling terms between heav y and light holes, By neglecting all small coupling terms it is possib le to describe the hole mixing at any stress in terms of independent t wo-level systems. In this case the Hamiltonian becomes block diagonal and can easily be diagonalized analytically. Within the experimentally accessible pressure range of 10 kbar, these simple analytic solutions deviate from the large-scale numerical solutions by less than 1%. The coupling of the spin-orbit split-off states in the Gamma(7) subspace to the Gamma(8) subspace at finite and zero stress is then taken into account via second-order perturbation theory. Comparison of the theore tical results with experimental photoluminescence data shows good agre ement and provides strong evidence for the stress-induced hole mixing.