Electron-interface-phonon interaction and magnetopolaronic impurity transitions in quantum wells

The polaronic effect on the hydrogenic 1s-2p₊ transition energy of a donor impurity located at the quantum well center in a double heterostructure is studied theoretically in detail. The electron-optical-phonon interaction Hamiltonian is derived on the basis of eigenmodes of lattice vibrations supported by the double heterostructure. Both the confined and interface phonon modes are included in the electron-phonon coupling. The transition energy is calculated as a function of the applied magnetic field for GaAs/Al_1-x Ga_xAs samples of well-widths d = 125 Å, 210 Å and 450 Å by the second-order perturbation. Wide transition gaps are predicted around the two-level and three-level resonances for all three cases. It is found that the transition gap narrows with the increasing well-width but remains larger than the LO and TO phonon frequency difference for d = 450 Å as is observed. We also perform the same calculation by assuming that the confined electron interacts with three-dimensional and two-dimensional phonon modes. The transition energy spectra from these calculations appear to be similar to those for a bulk sample, the spectrum splits at the resonance with the longitudinal optical phonon frequency only. From comparisons of our results with these calculations as well as with experiments, it is conclusively established that the wide gap of transition energy is solely due to the interface modes.