New exact results for the Hall coefficient and magnetoresistance of inhomogeneous two-dimensional metals

Several new theorems are proven for the magnetotransport coefficients of inhomogeneous normal-superconducting (N/S) and normal-insulating (N/I) films in a perpendicular magnetic field, under the assumption that macroscopic quantum effects such as Josephson coupling can be neglected. For N/S composites, at any field H, the Hall coefficient RH(p,H)∝(pc-p)²ˢ and the resistivity ρ(p,H)∝(pc-p)ˢ where p is the volume fraction of superconductor and pc is the percolation threshold. For N/I composites, as long as there is a connected metallic path across the sample, we show that both RH(p,H) and the ratio ρ(p,H)ρ(p,0) are independent of p and equal to the corresponding quantities for the normal metal.