${\mathit{D}}^{\mathrm{-}}$ states in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As superlattices in a magnetic field

The states of a negative donor center (${\mathit{D}}^{\mathrm{-}}$) located at the center of a quantum well (QW) of a GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As superlattice are investigated theoretically in a magnetic field applied along the growth axis. The energy levels of the ground (singlet ‖1s,1s;s〉) state and four excited (triplet ‖1s,2${\mathit{p}}^{\pm }$;t〉 states and the singlet ‖1s,2${\mathit{p}}^{\pm }$;s〉) state of the ${\mathit{D}}^{\mathrm{-}}$ center are obtained as functions of the magnetic field. The calculation is based on a variational approach in which we use trial wave functions with six variational parameters. We have investigated the influence of the following effects on the energy of the ${\mathit{D}}^{\mathrm{-}}$ states: (1) tunneling of the electrons into the adjacent wells of the superlattice, (2) electron-electron (e-e) correlation, and (3) the electron-phonon interaction. The magnetopolaron effect on these energies is studied within second-order perturbation theory. A detailed comparison is made between our theoretical results and available experimental data which are interpreted as transition energies between the ${\mathit{D}}^{\mathrm{-}}$ states. The effect of band nonparabolicity is of minor importance for most of the transition energies except for the transition from the ${\mathit{D}}^{\mathrm{-}}$ ground state to the ‖1s,2${\mathit{p}}^{+}$;s〉 state at high magnetic fields.