Hartree-Fock approximation for the quasiparticle properties of the coupled electron-phonon system in quantum-well wires in the presence of a magnetic field

A theory is presented that allows the calculation of the quasiparticle properties of lower-dimensional semiconductor nanostructures in the framework of a diagrammatic approach of many-particle Green's-function technique in subband space. We apply this theory to consider the interaction of quasi-one-dimensional electrons and longitudinal-optical (LO) phonons in the presence of a quantizing magnetic field. An expression for the electron matrix self-energy in subband space has been derived in the Hartree-Fock approximation of Feynman-Dyson perturbation theory. Numerical results for the energy-momentum relation and the effective mass have been obtained for the magnetopolaron states in quantum-well wires. It is shown that the Tamm-Dancoff approximation and its on-mass-shell version fail for the calculation of the renormalization of the excited subband energies in quantum-well wires with strong lateral confining potentials even for vanishing magnetic field and polaron momentum. In this case only the Hartree-Fock approximation gives the correct quasiparticle properties.