Electron–LO-phonon scattering near a current-carrying core

Abstract

A calculation is presented on the scattering rates of electrons via the bulk spectrum of longitudinal optical phonons near a current-carrying core of radius R employing the Fröhlich interaction Hamiltonian. The electrons are mainly confined near the core by an electric potential and are also under the influence of the current-induced spatially inhomogeneous static azimuthal magnetic field. The external magnetic field lifts 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. In fact, the k z < 0 electron’s energy subbands are found to be characterized by minima in their variations with the field. The intrasubband scattering rates show a remarkable behavior in their variations with the field. First, for weak electric potential of the nanosystem, these exhibit a strong, nonetheless inharmonic, oscillatory behavior in their variations with the field. The oscillations are, however, smoothed out as the strength of the electrical potential is increased, commencing at lower values of the field, within the same range of values of the field used. Second, for the same strength of the electric potential, there arise phase variations of the scattering rates in their variations with the field, resulting from the variation in the electron’s axial wave number.