MAGNETORESISTANCE OF 2-DIMENSIONAL MESOSCOPIC STRUCTURES - A VARIATIONAL APPROACH

We present a variational formulation for the scattering of charged par ticles in a two-dimensional multiport structure and in the presence of a magnetic field. Our approach can be applied to systems with any loc al potential function and with very mild restrictions on the magnetic field; in particular, it is not restricted to homogeneous fields. We a pply our approach to the calculation of the Hall, bend, and two-port r esistances over large ranges of magnetic fields and Fermi energies for a system of crossed quantum wires confined by hard and soft walls, an d in which a variety of impurity potentials have been placed. We find strong resonant features in these resistances for the case where a sin gle repulsive impurity is present in the center of the intersection, w hereas the resistances averaged over a random ensemble of potentials w ith nine impurities show a relatively weak effect. We also present res ults for scattering through a highly localized magnetic field in the i ntersection region.