Magnetoconductivity of quantum wires with elastic and inelastic scattering

Abstract

We use a Boltzmann equation to determine the magnetoconductivity of quantum wires. The presence of a confining potential in addition to the magnetic field removes the degeneracy of the Landau levels and allows one to associate a group velocity with each single-particle state. The distribution function describing the occupation of these single-particle states satisfies a Boltzmann equation, which may be solved exactly in the case of impurity scattering. In the case where the electrons scatter against both phonons and impurities we solve numerically - and in certain limits analytically - the integral equation for the distribution function, and determine the conductivity as a function of temperature and magnetic field. The magnetoconductivity exhibits a maximum at a temperature, which depends on the relative strength of the impurity and electron-phonon scattering, and shows oscillations when the Fermi energy or the magnetic field is varied.