Theory of Magnetic Breakdown,gFactor, and Energy-Band Structure of Zinc

The Landau levels associated with the "needle" in zinc have been studied by numerically solving the coupled differential equations given by applying the method of Luttinger and Kohn to Bennett and Falicov's k.p model. The "leakage" probability amplitudes and phases for tunneling from one monster through the needle to another monster agree with Pippard's semiclassical calculation. Thus, the Pippard network model and the magnetoresistance theory of Falicov, Pippard, and Sievert is justified. There is still some question as to the effect of magnetic breakdown on the de Haas-van Alphen amplitude associated with the needle. Because of the complicated Landau level structure, which comes from the near degeneracy of the bands, the various possible definitions of the $g$ factor do not agree. The data from the magnetoresistance, the de Haas-van Alphen effect, and the de Haas-van Alphen effect under pressure have been used to find two possible sets of energy-band parameters for the needle. Using a plausible definition of the $g$ factor, the band parameter solution which agrees most closely with other theoretical calculations corresponds to a $g$ factor of 170, while the other solution corresponds to $g=-170\mathrm{}$. An experimental selection of the correct solution would be provided by a measurement of the effect of pressure upon the breakdown field. The changes in the de Haas-van Alphen period and effective mass with alloying can be accounted for by reasonable changes in band parameters, but the predicted change in breakdown field is very different from the experimental results of Higgins and Marcus.