The Theory of the Anomalous Skin Effect in Anisotropic Metals

The theory of the anomalous skin effect in metals is extended to a uniaxial metal crystal containing two energy bands in each of which the energy surfaces are ellipsoids of revolution about the crystal axis. Explicit formulae are obtained, for the extreme anomalous limit, giving the dependence of the surface impedance on the orientation of the crystal axis, both for a plane metal surface and for a circular wire. The form of the anisotropy of the surface impedance is found to depend upon the axial ratios of the spheroidal energy surfaces and upon the ratio of the electron free paths in the two bands. Wide variations in behaviour are possible, and the surface impedance may show a high degree of anisotropy even when the d.c. conductivity is almost isotropic (as with tin at low temperatures). The results are evaluated numerically for tin, and the surface conductivity of a circular wire is found to show the minimum observed by Pippard (1950); the parameters can be chosen to give reasonable agreement with Pippard’s results.