Hydrostatic-pressure-induced Γ-X mixing in delta-doped Al_xGa_1-xAs

The mixing between Γ and X points in the conduction band is known to manifest in GaAs/Al_xGa_1-xAs heterostructures. Application of hydrostatic pressure leads to the variation of both the Γ- and X-energy gaps in such a way that around P = 39 kbar, the GaAs becomes an indirect gap one. Within a narrow interval of P around this value, both minima remain almost energetically aligned. Therefore, it can be expected that some kind of mixing between the states corresponding to the delta-quantum-wells formed at those points should manifest. In this work, we investigate the occurrence of Γ-X mixing induced by the application of hydrostatic pressure in n-type delta doped Al_xGa_1-xAs, by means of a variational scheme that uses a 2×2 Hamiltonian with the off-diagonal element being a variational potential energy. Diagonal Schrödinger-like effective mass elements are written with potential functions given by the Thomas-Fermi approximation. The effect of the hydrostatic pressure is incorporated via the dependence on P of the different input parameters in the system: energy gaps, effective masses and dielectric constant. We report the variation of the ground state of the system as a function of P.