Shubnikov-de Haas Measurements in Bismuth

Abstract

The oscillatory transverse magnetoresistance (Shubnikov---de Haas effect) has been measured for the magnetic field in the binary and trigonal planes of single-crystal bismuth at liquid-helium temperatures, using a technique which permits accurate identification and determination of the periods and measurement of the amplitudes. Periods observed in high-purity samples [resistivity ratios $(\frac{{R}_{300 ^{\ensuremath{\circ}}\mathrm{K}}}{{R}_{4.2 ^{\ensuremath{\circ}}\mathrm{K}}})\ensuremath{\gtrsim}400$] can be fit to the generally accepted Fermisurface model of one hole ellipsoid and three tilted electron ellipsoids. For resistivity ratios $\ensuremath{\lesssim}300$, additional periods are observed which recently have been shown to be caused by twinning. The effects of twinning, together with the difficulty in interpreting oscillatory resistivity data taken by traditional techniques, are suggested as explanations for the many spurious periods reported in the literature and used as arguments for additional pieces of the Fermi surface. By fitting the amplitudes of the oscillations to the theory for the magnetoresistance of an electron gas with level (Dingle) broadening, the Dingle temperatures of holes and electrons were found to be (0.7\ifmmode\pm\else\textpm\fi{}0.2) and (0.4\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode^\circ\else\textdegree\fi{}K, respectively. These values are comparable with earlier results of Bhargava from de Haas-van Alphen (thermodynamic as opposed to transport) measurements, but are 50 times larger than the values estimated from zero-field conductivity. Agreement within a factor of 2 is obtained when the increased scattering of carriers in the highest Landau level, due to their low velocities along the magnetic field, is considered.