Electronic states in quasi-one-dimensional wires with nonuniform magnetic fields

We have investigated the transmission of an electron in quasi-one-dimensional systems in the presence of nonuniform magnetic fields. The subband energy and the wave function in a magnetic field, whose strength varies parabolically in the transverse direction, are calculated. This model is expected to describe a composite fermion in quantum wires. The parabolic magnetic field is found to increase the band-edge energies and modify the probability distribution significantly. When a moderate negative offset magnetic field is added, the subband energy takes a minimum value for a finite parabolic magnetic-field strength and the wave function of the lowest subband is double peaked. We have calculated magnetic-field dependencies of the bend resistance and the Hall resistance in a cross junction, in which the parabolic magnetic field is assumed. The positions in magnetic field of the peak in the bend resistance due to ballistic transport and of the zero Hall resistance are shifted and generally do not coincide as the parabolic field is imposed. We also examine the conductance of quantum wires in the presence of random magnetic fields. The nonuniform magnetic fields lead to universal conductance fluctuations in the metallic regime and to exponential decay of the conductance as the length is increased in the localized regime. In contrast to the impurity scattering case, the localization length is found to be smaller for larger average magnetic fields.