Band Structure of Aluminum

Calculations of the band energies at symmetry points in aluminum by Heine are extended into the zone using the pseudopotential interpolation scheme in order to obtain constant-energy curves in the neighborhood of the Fermi surface. In conjunction with this calculation, the lines of contact between various bands are found in detail. The de Hass-van Alphen effect, cyclotron-resonance effect, anomalous skin effect, and low-temperature specific heat are discussed in terms of these constant-energy curves and the results compared with experiment. It appears from this comparison that the geometry of the Fermi surface is given quite well by the band calculations, but that there is a discrepancy of a factor of order two between the derived and measured effective masses. A "single orthogonalized-plane-wave approximation" is compared with the more exact treatment and found to be a good starting approximation, suitable for semiquantitative treatment of the electronic structure.