Effect of subband mixing on the energy levels of a hydrogenic impurity in a GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As double quantum well in a magnetic field

In view of the recent evidence found in favor of subband mixing in coupling of confined impurity states in doped double-quantum-well structures, a variational approach employing Gaussian trial wave functions has been used to calculate the binding energies of the ground, (1s, m=0) and first excited, (2${\mathit{p}}_{\mathrm{-}}$, m=-1) states of a hydrogenic donor associated with the mixture of subbands of a double-GaAs quantum well coupled by a layer of ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{A}1\mathrm{}}_{\mathit{x}}$As in the presence of a magnetic field. Two different well sizes and three different locations of the impurity, (A) at the outer edge, (B) at the center, and (C) at the inner edge of the well, are considered, and the barrier width is allowed to vary. It is found that for the structures considered here the results from the calculations using the mixture of only first (symmetric) and second (asymmetric) subbands are significantly different from those using only the lowest (symmetric) subband, especially for the intermediate barrier widths, and depend strongly on the location of the impurity in the well. These results demonstrate that subband mixing should be included in double-quantum-well structure calculations. The effect of varying the magnetic field on the binding energies is also studied. A comparison with the measurements of Ranganathan et al. [Phys. Rev. B 44, 1423 (1991)] demonstrates that the agreement is not improved when mixing of subbands higher than the lowest two is included in the calculation.