Excited states of the two-dimensional ${\mathit{D}}^{\mathrm{-}}$ center in magnetic fields

Excited states of the two-dimensional ${\mathit{D}}^{\mathrm{-}}$ center (or ${\mathrm{H}}^{\mathrm{-}}$ ion) are considered in the low-field and high-field limits. It is shown that in two dimensions there are no bound analogs of the large-radius bound excited states that spring into existence when an arbitrarily weak magnetic field is applied to a three-dimensional ${\mathrm{H}}^{\mathrm{-}}$ ion. Asymptotically exact wave functions and energies are obtained in the limit of infinite magnetic field. In that limit, only four bound states are found in two dimensions: one spin singlet (symmetric space wave function), which is the ground state, and three spin triplets (antisymmetric space wave functions). It is pointed out that even those states that are unbound have, nevertheless, discrete energy levels in two dimensions (due to the Landau quantization of the planar motion) and play an essential role in the absorption of radiation by the ${\mathit{D}}^{\mathrm{-}}$ center. Connections between the two-dimensional ${\mathit{D}}^{\mathrm{-}}$ center and ${\mathit{D}}^{\mathrm{-}}$ centers in quantum wells are discussed.