Shubnikov-de Haas Effect in Bismuth

Abstract

The oscillatory component of the transverse magnetoresistance of bismuth has been measured as a function of magnetic field orientation at liquid helium temperatures. A derivative technique was employed. In addition to sets of periods, observed in the de Haas-van Alphen effect by Shoenberg and by Brandt and attributed by them, respectively, to the electron and light-hole Fermi surfaces, we observe a new set of isotropic short periods, $P=0.72\mathrm{}\times {10}^{-5\mathrm{}}$ ${\mathrm{G}}^{-1\mathrm{}}$. The squares of the electron Fermi momenta $m_0{{\kappa }_{11}}^2$, $m_0{{\kappa }_{22}}^2$, $m_0{{\kappa }_{33}}^2$, $m_0{{\kappa }_{23}}^2$ are, respectively, 0.189, 45.4, 0.918, and $-4.54\mathrm{}{m}_0$ milli-electron volts (meV). For the light holes, $m_0{{\kappa }_{11}}^2$ and $m_0{{\kappa }_{33}}^2$ are 1.51 and $21.0m_0$ meV. For the new heavy carriers, $m_0{\kappa }^2=3.18\mathrm{}{m}_0$ meV. These data are fitted to two possible three-carrier models of the Fermi surface, and to a four-carrier model. Significant deviations of the oscillations from periodicity in $H^{-1\mathrm{}}$ are observed for the electron part of the Fermi surface for certain magnetic field orientations.