Magnetoresistance of two-dimensional mesoscopic structures: A variational approach

We present a variational formulation for the scattering of charged particles in a two-dimensional multiport structure and in the presence of a magnetic field. Our approach can be applied to systems with any local potential function and with very mild restrictions on the magnetic field; in particular, it is not restricted to homogeneous fields. We apply our approach to the calculation of the Hall, bend, and two-port resistances over large ranges of magnetic fields and Fermi energies for a system of crossed quantum wires confined by hard and soft walls, and in which a variety of impurity potentials have been placed. We find strong resonant features in these resistances for the case where a single repulsive impurity is present in the center of the intersection, whereas the resistances averaged over a random ensemble of potentials with nine impurities show a relatively weak effect. We also present results for scattering through a highly localized magnetic field in the intersection region. © 1996 The American Physical Society.