Magnetotransport in a parabolic channel exposed to a periodically modulated magnetic field

We have studied the energy spectrum and magnetotransport of a parabolic one-dimensional channel in the presence of periodic modulations in both magnetic field and the electrostatic potential. The periodic modulations change the sub-band energy-wave-vector relation and produce mini-gaps at specific wave-vectors. The gaps exist even if there is only modulation in the magnetic field. For the cases where the two kinds of modulation are in phase or out of phase, we give the explicit expressions for the values of the gaps. In the ballistic transport regime, the conductance is expected to remain quantized and to evolve in a simple manner as a function of the Fermi energy. Starting from linear response theory, the transport properties are studied numerically, taking into account the impurity scattering. Calculations related to magnetic field modulation show that a series of cusps in the conductance are produced, whose magnitude depends strongly on the degree of impurity scattering. The structure of these cusps can be explained in terms of the energy band structure.