An experimental determination of the Fermi surface in copper

Abstract

Measurements have been made of the variation with crystal orientation of the anomalous skin resistance of plane surfaces of pure copper at low temperatures and at a frequency of 22700 Mc/s. The resistance is related to the geometrical form of the Fermi surface, and a surface is determined which has the correct shape to account for the experimental results. It is believed that there is no other solution which would give equally good agreement. As determined, the surface, which holds one electron per atom, will not quite fit into the Brillouin zone, overlapping in the (111) directions where the zone boundary is closest to the origin. From an examination of simple models it is concluded that probably there is contact with the zone boundary over small areas around these points, and the energy gap across these boundaries is estimated to be about 71/2 eV. Apart from extension to the boundaries in the (111) directions the Fermi surface is more or less spherical. An estimate is made of the Fermi velocity and its variations over the surface, from which it is concluded that the electronic specific heat should lie between 1.7 and 1.9 times that of a free-electron model of copper. The experimental value is 1.38, and it is tentatively suggested that the discrepancy may find an explanation in the theory of Bohm & Pines. Various transport phenomena are briefly discussed, but no reliable evidence is discovered bearing directly on the shape of the Fermi surface. It is concluded that the method, though laborious in interpretation, may be applied with advantage to other simple metals such as silver and gold.