Electron Transport Phenomena in Bismuth at Liquid-Helium Temperatures

Abstract

Transport effects were studied in a bismuth single crystal at liquid-helium temperatures in a magnetic field. Except for a field-orientation study of the galvanomagnetic effects for mapping the light-holes ellipsoid, all the measurements were taken in the basal plane of the crystal with the field parallel to the trigonal axis. The thermal conductivity was found to be almost entirely due to lattice conductivity; therefore, the experimental coefficients determined were limited to the following: the isothermal transverse magnetoresistivity ${\rho }_{11}$, the isothermal Hall resistivity ${\rho }_{21}$, the (adiabatic) thermoelectric coefficient ${{\epsilon }_{11}}^{\prime }$, the (adiabatic) Nernst-Ettinghausen coefficient ${{\epsilon }_{21}}^{\prime }$, and the transverse magnetothermal resistivity ${\gamma }_{11}$. The Peltier tensor coefficients were expected (from the Onsager relations) to be too small to be measurable and thus, were not studied here. All these effects, except the thermal resistivity coefficient exhibit the Schubnikov-de Haas type oscillations. The kinetic coefficients of the transport effects ${\sigma }_{11}$, ${\sigma }_{12}$, ${{\epsilon }_{11}}^{\prime \prime }$, and ${{\epsilon }_{12}}^{\prime \prime }$ were computed from the experimental coefficients and compared with available theories. A rough analysis of the gross effects was made by a decomposition of each coefficient into a sum of different band contributions, each band being approximated by a Lorentz term. General, but not complete, agreement between experiment and theory is achieved for both two-band and multiband models. No special mechanism (i.e., like that proposed for zinc) is needed to explain the oscillations in the different effects, since the Lifshitz and Kosevich theory (${\sigma }_{12}$), the Zil'berman theory (${\sigma }_{11}$, ${{\epsilon }_{11}}^{\prime \prime }$), and the influence of oscillation in the density of states (${{\epsilon }_{12}}^{\prime \prime }$) lead to satisfactory agreement with the experiments.