Galvanomagnetic Properties of a Nonellipsoidal Nonparabolic Band Model. II. Weak-Field Magnetoresistance

Abstract

The weak-field magnetoresistance is calculated for three cubically symmetric versions of Cohen's multivalley model (originally derived for Bi) in which the valleys are surfaces of revolution along the $〈111〉$, $〈100〉$, and $〈110〉$ directions of momentum space. The Jones-Zener weak-field solution of the Boltzmann equation, an isotropic scattering time, and degenerate statistics are assumed. The Seitz coefficients $b$, $c$, and $d$ and the symmetry parameter $z (b+c+zd=0)$ were computed for about 3000 values of the energy and mass parameters $\ensuremath{\epsilon}$ and $\ensuremath{\mu}$ which cause the model to become nonellipsoidal and nonparabolic. Graphs of the results are presented for selected values of $\ensuremath{\epsilon}$ and $\ensuremath{\mu}$. For $\ensuremath{\mu}=1$, the $z$ values are precisely the same (0, \ifmmode\pm\else\textpm\fi{} 1) as in the corresponding ellipsoid-of-revolution parabolic models. Otherwise, $|z|$ deviates only slightly ( 0.3) from the simple values for wide ranges of $\ensuremath{\epsilon}$ and $\ensuremath{\mu}$, including the range in which the Fermi surface acquires a very distorted dumbbell shape. The only exception is a peak in $z$ which occurs for $\ensuremath{\mu}1$ when the energy surfaces are nearly isotropic and $b$, $c$, and $d$ are all small. Experimental values of $z$ in highly degenerate samples of $p$-type SnTe lie between - 1 and - 6, the coefficient $b$ is large, and the Fermi surfaces in this compound are known to be strongly prolate and $〈111〉$ oriented. Hence the Cohen model, when used with the above-mentioned restrictions, cannot account for the experimental weak-field magnetoresistance in SnTe. The significance of this result, as well as some modifications which might bring theory and experiment closer together, is discussed.