Fermi Surface and Energy Bands of Copper

The Green's function method has been used to study the energy bands of Cu for two quite different potentials. It is found that the resulting $E\left(\mathrm{k}\right)$ for the two cases are very similar throughout the Brillouin zone having the same ordering of the levels and comparable level separations in the conduction, low-lying excited, and $d$-band regions. This implies that the calculated band structure is not as sensitive as had been previously contended. The properties of the Fermi surfaces associated with the two theoretical band structures are compared with the results of experimental studies. It is found that the theoretical surfaces intersect the hexagonal zone face in accord with experiment. The computed radii of contact for the two cases are close to the measured values. Furthermore, the bellies for the two cases are shown to deviate appreciably from sphericity in agreement with the results of recent magnetoacoustic effect experiments. The origin of the distortions is explained in terms of the interaction between the conduction and $d$ bands. The "masses" defined in terms of the cyclotron resonances for various orbits on the Fermi surface, the lowtemperature electronic specific heat, and the dielectric constant in the infrared region are determined for the calculated $E\left(\mathrm{k}\right)$. The calculated masses are all somewhat lower (by about 10-30%) than the corresponding measured masses. It is believed that these discrepancies reflect the contributions of the effects neglected in the individual-electron model. Finally, the sharp rise in the optical absorption, which on the basis of the theoretical $E\left(\mathrm{k}\right)$ corresponds to the onset of interband transitions between the $d$ bands and the Fermi level, is found to occur at an energy in good accord with experiment.