Conductance of a quantum wire in a parallel magnetic field

Ballistic electron transport in a three-dimensional quantum wire with ellip tic cross section is investigated. The potential of the single-particle Ham iltonian of the system under consideration was chosen to be parabolic. Usin g the Landauer-Buttiker formalism, we find an expression for the conductanc e at zero temperature. We show that the number and width of the steps in th e dependence of the conductance on the electron energy are determined by th e 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 oscillatin g second term gives sawtooth-shaped peaks. The height of the conductance st eps is equal to the conductance quantum, and the width of the plateau depen ds on the energy, the field, and the frequency ratio. We stress that the pi cture of the conductance is extremely sensitive to the ratio of hybrid freq uencies. (C) 1999 American Institute of Physics. [S1063-7826(99)03109-9].