Band Structure and Fermi Surface of Beryllium

Using a self-consistent potential, the energy eigenvalues along the symmetry edges, on the zone faces, and at the equivalent of 5184 general points in the first Brillouin zone were calculated for beryllium by expanding the conduction electron wave functions in a linear combination of 23 orthogonalized plane waves. From this the Fermi energy and density of states were calculated and the Fermi surface constructed. The density of states is in agreement with soft x-ray emission and absorption data and with the experimental low-temperature specific heat coefficient. The Fermi surface consists of three pieces: A region of unoccupied states in the first double zone which resembles a coronet, and two identical pockets of electrons in the second double zone similar in shape to a cigar with a triangular cross section. The de Haas-van Alphen frequencies in $\frac{1}{H}$ predicted from the Fermi surface are in good agreement with those measured experimentally.