Magnetopolarons in quasi-one-dimensional quantum-well wires

Abstract

The interaction of quasi-one-dimensional electrons and longitudinal-optical (LO) phonons in the presense of a quantizing magnetic field is calculated. Results are detailed presented for the polaron correction to the subband energies, the polaron cyclotron mass and the polaron effective mass. The calculations are done by using different approaches, Rayleigh–Schrödinger perturbation theory, Wigner–Brillouin perturbation theory, improved Wigner–Brillouin perturbation theory and Green's function technique. In the framework of a diagrammatic approach a modified Hartree–Fock approximation is developed, which allows the calculation of the quasi-particle properties of lower-dimensional semiconductor nanostructures in the subband space. It is shown that the Rayleigh–Schrödinger perturbation theory, improved Wigner–Brillouin perturbation theory and the modified Hartree–Fock approximation well describe the ground-state renormalization, but only the improved Wigner–Brillouin perturbation theory and the modified Hartree–Fock approximation well describe the bend-over and pinning behaviour of the subbands at the boundary of the phonon continuum. Rayleigh–Schrödinger and Wigner–Brillouin perturbation theories fail for the calculation of the renormalization of the excited subband energies in quantum-well wires with strong confining potential even for vanishing magnetic field and polaron momentum. In addition to the symmetric scattering processes, which are the only processes involved in the self-energy of the old-fashioned perturbation theories, Green's function technique allows also to calculate the contribution of all asymmetric scattering processes of two electrons by exchanging an optical phonon.