Quantum Oscillations in the Peltier Effect of Zinc

Peltier measurements have been employed to study quantum oscillations in the thermoelectric power of zinc single crystals. The three lowest frequencies, due to the $\alpha$, $\beta$, and $\gamma$ orbits, were observed at temperatures ranging from 1.2 to 4.5°K and in fields to 22 kG. The amplitudes found were between 0.01 and 1 μV/K°. An attempt has been made to correlate these measurements with an expression derived by Horton. As his calculation is valid only for the case of a free-electron sphere, his results have been heuristically extended to include metals with complex Fermi surfaces. The theory and measurements agree only in the form of the temperature dependence; neither the absolute amplitudes nor the field dependence is correctly predicted by the theory. It is suggested that the disagreement may arise from the assumption of independent bands in the extension of Horton's single-band calculation. In particular, the oscillating density of states gives rise to a strongly energy-dependent relaxation time, which may significantly affect the thermoelectric power. An approximate calculation of the oscillation amplitude to be expected from this mechanism is presented. Although the agreement with the data is again not perfect, there are some qualitative indications that favor this model. Experiments in a longitudinal configuration should shed further light on the problem, and such experiments are now in progress.