Magnetoconductivity of quantum wires with elastic and inelastic scattering

TL;DR

This paper investigates how quantum wires' magnetoconductivity varies with temperature and magnetic field, considering impurity and phonon scattering, revealing maxima and oscillations in conductivity.

Contribution

It provides an exact solution for impurity scattering and a numerical approach for combined impurity and phonon scattering in quantum wires.

Findings

Magnetoconductivity shows a maximum at a specific temperature.

Conductivity exhibits oscillations with changes in Fermi energy or magnetic field.

The study models the effects of impurity and phonon scattering on quantum wire transport.

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.