Magnetic Energy Levels in an Energy Band with Inversion Asymmetry Splitting

We consider an energy band which is spherical except for a term giving the inversion asymmetry splitting possible in the zinc-blende structure. This splitting is small but very anisotropic, so that the classical cyclotron orbits on the split Fermi surfaces are complicated and sometimes cross. We solve for the magnetic levels of the system when the magnetic field is along the three principle directions. The results for $〈111〉$ and $〈100〉$ differed considerably from the classical picture. The calculation supports the proposal of Groves and Wyatt that the beating observed in the Shubnikov-de Haas effect in HgSe by Whitsett is due to inversion asymmetry splitting. The beat pattern was fairly well accounted for. A splitting parameter $\gamma$ of 0.085 was found for Whitsett's 1.3×${10}^{18}$-${\mathrm{cm}}^{-3\mathrm{}}$ sample, where $\frac{1}{2}\gamma k_F$ is the maximum radial splitting of the Fermi surface.