De Haas—Van Alphen Effect and Fermi Surface in Arsenic

A detailed and accurate study of the de Haas-van Alphen effect and Fermi surface of arsenic has been made by a vector-modulation technique. We find two sets of Fermi surfaces which together give the required volume compensation. The first set contains three closed, centrosymmetric pockets ($\beta$ in our notation) which have a tilt angle (for the minimum area) of 86.4±0.1° from the trigonal axis. Their total volume is found to be (2.12±0.01) × ${10}^{20}$ carriers/${\mathrm{cm}}^3$. The other set forms a single multiply connected surface of symmetry $\overline{3}m$ and consists of six $\alpha$ pockets (the Berlincourt carriers) which have a tilt angle of 37.25±0.1°, and which are connected together by six long thin necks with a tilt of -9.6±0.1°. This is in excellent agreement with the recent pseudopotential calculation by Lin and Falicov if the $\beta$ pockets are due to electrons at $L$ and the multiply connected surface to holes around $T$. The multiplicities of the pockets are deduced from the experimental data and are supported by the consequent satisfactory agreement with the observed electronic specific heat.