Theory of the Hall effect in quantum wires: Effects of scattering

Abstract

Effects of scattering and Hall-probe geometry on the Hall effect are studied in quantum wires. Scattering modifies the Hall effect through a change in the current distribution among the subbands. Explicit calculations of the current distribution and the Hall resistance are made using the Boltzmann transport equation for scattering from impurities and boundary roughness in several geometries of the Hall probes, weak-link models, and crossed-wire geometry. At high magnetic fields plateaus of the Hall resistance show a slope as a function of the magnetic field due to the finite-size effect. The gradient of the slope and the value of the magnetic field at a jump between plateaus depend on the geometries of the Hall probes and kinds of scatterers as well as the wire width. At low magnetic fields the Hall resistance is quite sensitive to the geometry of the Hall probes. In the crossed-wire geometry, boundary-roughness scattering gives rise to a considerable suppression of the Hall resistance.