Scattering of electrons via bulk LO-phonon modes near a cylindrical core under the influence of an external azimuthal magnetic field

Abstract

An investigation is carried out of the interactions of electrons with longitudinal optical (LO) phonons under the influence of an azimuthally directed external magnetic field. The magnetic field is thought to be induced by a steady current passed along the axis of an infinitely long cylindrical core of radius R . Confinement of electrons to regions near the core is assumed to be due to a parabolically varying electric potential of the heterojunction. As anticipated, the azimuthal magnetic field is found to lift the double degeneracy of the non-zero electron's axial wave number ( k z ) states while that of the non-zero azimuthal quantum number ( m ) states is preserved. Furthermore, the azimuthal magnetic field breaks the parabolicity symmetry in k z of the electron's energy subbands. Notably, as the field is increased, the k z < 0 branch of the electron's energy subband is systematically lowered and this is accompanied by a shift of the electron's subband energy minimum to higher values of | k z | . The scattering rates of electrons via bulk LO-phonon modes are obtained employing the Fröhlich interaction Hamiltonian. The intrasubband scattering integrals are found to be characterized by strong oscillations in their variations with the phonon radial wave number, nevertheless, enveloped by a rapid decay of their amplitudes. The intrasubband emission scattering rates exhibit a divergent behaviour for electron energies very near the LO zone frequency, reminiscent of the character of quasi-one-dimensional electronic states. In contrast to the axial applied magnetic field configuration, again, the azimuthal magnetic field breaks the symmetry of the ± k z branches of the intrasubband scattering rates. In general, the k z < 0 branch of the scattering rates is found to be systematically more depressed compared to that of the corresponding positive electron's wave number.