Galvanomagnetic properties of cylindrical fermi surfaces

Abstract An infinite cylinder has the same general properties, with respect to the connectivity of its plane sections, as the Fermi surface proposed by Pippard (1957) for copper. For this model, the conductivity tensor in an arbitrary magnetic field H is calculated exactly, and then averaged over all orientations of the cylinder axis relative to H. This is taken, without proof, to represent the bulk conductivity of a polycrystalline specimen. It agrees remarkably well, both at low and high fields, with the experimental results on copper, especially in making the transverse magnetoresistance proportional to H. This can be understood physically. There are always some crystallites, specially oriented to the field, where the orbits in k-space are open, or so extended that they are not traversed in the relaxation time. Since some of their conductivity components remain finite they provide leakage paths for the current but, as H increases, their number decreases as I/H. The observed saturation of the longitudinal magnetoresistance may also be explained by reference to the true Fermi surface and a slight sophistication of the model.