Deviations from Quantized Hall Conductivity and Current Density Distribution in Finite 2DEG Samples

Simple expressions for local and total Hall conductivities in finite two dimensional electron systems under magnetic field are obtained from the Kubo formula. The deviations of the Hall conductivity from integer values are always negative and their magnitude is inversely proportional to the effective width of the sample and proportional to the slope of the Landau branch dispersion relation at the Fermi level, Eq. (22). We also calculate the local conductivity in finite samples. The conductivity density is constant in the bulk and sums up to an integer value. Its spatial distribution is terminated in the bulk in a universal manner. Illustrations for simple models of the confinement barrier, as well as relation to recent experimental data for quantum wires are given.