Theory of Hall Effect in a Two-Dimensional Electron System

;
• Matsumoto, Yukio
;
• Uemura, Yasutada

Abstract

Hall conductivity σ_XY is studied in various approximations. Characteristics of σ_XY are obtained for the case of both short- and long-ranged scatterers in the self-consistent Born approximation, which is the simplest one free form the difficulty of divergence. In case of short-ranged scatterers, a relation is shown to hold between σ_XY and σ_XX within this approximation, if one uses a relaxation time under magnetic fields. Under strong magnetic fields, effects of higher Born scattering become important in low-lying Landau levels. They depend on the sign of scatterers and strongly on their concentrations. Effects of simultaneous scattering from many scatterers are calculated to the lowest order.