De Haas—Van Alphen Effect and Fermi Surface in Arsenic

Abstract

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 ($\ensuremath{\beta}$ in our notation) which have a tilt angle (for the minimum area) of 86.4\ifmmode\pm\else\textpm\fi{}0.1\ifmmode^\circ\else\textdegree\fi{} from the trigonal axis. Their total volume is found to be (2.12\ifmmode\pm\else\textpm\fi{}0.01) \ifmmode\times\else\texttimes\fi{} ${10}^{20}$ carriers/${\mathrm{cm}}^{3}$. The other set forms a single multiply connected surface of symmetry $\overline{3}m$ and consists of six $\ensuremath{\alpha}$ pockets (the Berlincourt carriers) which have a tilt angle of 37.25\ifmmode\pm\else\textpm\fi{}0.1\ifmmode^\circ\else\textdegree\fi{}, and which are connected together by six long thin necks with a tilt of -9.6\ifmmode\pm\else\textpm\fi{}0.1\ifmmode^\circ\else\textdegree\fi{}. This is in excellent agreement with the recent pseudopotential calculation by Lin and Falicov if the $\ensuremath{\beta}$ 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.