GEOMETRIC INTERPRETATION OF THE WEAK-FIELD HALL CONDUCTIVITY IN 2-DIMENSIONAL METALS WITH ARBITRARY FERMI-SURFACE

The Hall conductivity sigma-xy of a two-dimensional metal in the weak-field, semiclassical, limit has a simple geometric representation. Sigma-xy (normalized to e2/h, where e is the electron charge and h is Planck's constant), is equal to twice the number of flux quanta phi-O threading the area A(l), where A(l) is the total "Stokes" area swept out by the scattering path length l(k) as K circumscribes the Fermi surface (FS). From this perspective, many properties of sigma-xy become self-evident. The representation provides a powerful way to disentangle the distinct contributions of the three factors, FS area-to-circumference ratio, anisotropy in l(k), and negative FS curvature. The analysis is applied to the Hall data on 2H-NbSe2 and the cuprate perovskites. Previous model calculations of sigma-xy are critically reexamined using the new representation.