Quantum oscillations and Fermi surfaces of Sn- and Pb-doped Bi

Abstract

The Fermi surfaces of bismuth single-crystal samples doped with tin and lead have been investigated by means of the techniques of ultrasonic quantum oscillations (UQO) and Shubnikov-de Haas (SdH) oscillations. Experiments were carried out in the temperature range 1.2-4.2 K using longitudinal ultrasonic waves of frequencies up to 70 MHz and in magnetic fields up to 2.3 T. The excess hole densities of single-crystal samples obtained from the analysis of UQO and SdH oscillations data, residual resistivity ratio (RRR) and Hall-effect measurements are in the range of 3*1023 to 1.4*1025 m-3. The Fermi-surface geometry of carriers was determined from the angular dependence of the periods of UQO and SdH oscillations. The major effect of doping of bismuth with Sn (or Pb) is to decrease the Fermi energy. On increasing the amount of doping, the pockets in the L-point conduction band became progressively smaller. Further increase of the dopant concentration leads to the disappearance of the L-electron pockets and the appearance of L holes. The experimental results have shown that the Fermi surfaces of acceptor-doped bismuth crystals are similar to those of pure bismuth and that the Lv valence band is the mirror image of the Lc conduction band.