Electron Transport Phenomena in Zinc at Liquid-Helium Temperatures

Abstract

The magnetic-field dependences of the electrical and thermal resistances, the thermoelectric power, the Hall, the Righi-Leduc, the Peltier, the Ettingshausen, and the Ettingshausen-Nernst effects at liquid-helium temperatures in magnetic fields up to 14 kG, have been investigated in a single crystal of zinc. The measurements were taken with either a constant heat current or a constant electric current flowing perpendicular to the hexagonal axis and with the magnetic field parallel to the hexagonal axis. Original observations of de Haas-van Alphen type oscillations were made in the Righi-Leduc, the Peltier, and the Ettingshausen effects. Respective periods of 6.14, 6.28, and 6.45\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ ${\mathrm{G}}^{\ensuremath{-}1}$ were found. Like the Hall effect, the Righi-Leduc effect changes sign at about 5500 G. The Ettingshausen and the Peltier effects are strongly oscillatory with little monotonic variation with field. The oscillations in the Peltier effect and the thermal magnetoresistance exhibit a phase inversion near 5000 G similar to that in the Ettingshausen-Nernst effect and the magnetoresistance. This change in phase is correlated with the change in sign of the Hall and the Righi-Leduc effects at about the same field value. The longitudinal and transverse Lorenz ratios are equal and remain practically constant in high fields at a value of 2.35\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ ${\mathrm{V}}^{2}$${/\mathrm{d}\mathrm{e}\mathrm{g}}^{2}$, i.e., 4% smaller than the free-electron value. An extrapolated value of the lattice conductivity at 2\ifmmode^\circ\else\textdegree\fi{}K is 0.02 W/deg-cm, i.e., about 0.02% of the zero-field electronic thermal conductivity. The thermoelectric effects are compared by means of the Onsager relations. Excellent agreement is found for the phase and amplitude of oscillations. The different kinetic coefficients relating fluxes to affinities were computed to facilitate comparison with theory. Curve fitting of the conductivity coefficients to Sondheimer-Wilson theory was attempted in terms of a four-band scheme. Analysis of the oscillations was attempted in terms of recent theory. The Righi-Leduc and the Hall conductivities, the Ettingshausen-Nernst, and the Ettingshausen effects (the transverse effects) strongly disagree with the expectation of any of the available theories, each exhibiting oscillations whose amplitude is several orders of magnitude larger than that calculated from any of the various theories. The results for the longitudinal effects (the thermal and the electrical conductivities, and the thermoelectric and the Peltier coefficients) are consistent, within the experimental error, with recent quantum-mechanical conductivity theories.