Conductance of a quantum wire in a parallel magnetic field

Ballistic electron transport in a three-dimensional quantum wire with elliptic cross section is investigated. The potential of the single-particle Hamiltonian of the system under consideration was chosen to be parabolic. Using the Landauer-Buttiker formalism, we find an expression for the conductance at zero temperature. We show that the number and width of the steps in the dependence of the conductance on the electron energy are determined by the ratio of the characteristic frequencies of the potential. In the case of nonzero temperature we show that the conductance consists of two terms. The first is monotonic and depends quadratically on the energy; the oscillating second term gives sawtooth-shaped peaks. The height of the conductance steps is equal to the conductance quantum, and the width of the plateau depends on the energy, the field, and the frequency ratio. We stress that the picture of the conductance is extremely sensitive to the ratio of hybrid frequencies.