Current, potential, electric field, and Fermi carrier distributions around localized elastic scatterers in phase-coherent quantum magnetotransport

The spatial distributions of the current, Fermi carriers, electric field (due to space charges) and electrostatic potential in a disordered mesoscopic structure are calculated in the presence of arbitrary magnetic fields. These distributions are useful in elucidating and visulaizing many features of quantum magnetotransport, such as the formation of edge states at high magnetic fields and their near-perfect transmittivity, the evolution of the integer quantum Hall effect, the creation of magnetic bound states around an impurity, the magnetic response of current vortices that form as a result of quantum interference between scatterers and the walls of a quantum wire, the dependence of the quantized-conductance steps in a backgated quantum wire on an applied magnetic field, the behavior of residual-resistivity dipoles and the electrostatic space-charge potential in a magnetic field, the dependence of the sign of the magnetoresistance on the impurity configuration, etc. We examine the current, Fermi carrier concentrations, electric field, and both chemical- and electrostatic-potential profiles associated with each of these phenomena, and relate them to the observed terminal characteristics in each case.