Theory of the Valence Band Structure of Germanium in an External Magnetic Field

Abstract

The energies of the magnetic sub-bands associated with the ${V}_{1}$ and ${V}_{2}$ valence bands in germanium have been calculated as a function of ${k}_{z}$, the propagation constant parallel to the external magnetic field. Warping of the ${V}_{1}$ and ${V}_{2}$ bands was neglected. Sub-bands belonging to the ${1}^{+}$ and ${2}^{+}$ ladders (light holes) have minima at ${k}_{z}=0$ and show quantum effects consisting of a decrease in curvature as the valence band edge is approached. Sub-bands belonging to the ${2}^{\ensuremath{-}}$ ladder (heavy holes) also have minima at ${k}_{z}=0$, but the curvatures increase near the valence band edge. The ${1}^{\ensuremath{-}}$ heavy hole sub-bands show very marked quantum effects. The sub-band minima occur at values of ${k}_{z}$ different from zero, and local maxima appear at ${k}_{z}=0$. The peculiar nature of the ${1}^{\ensuremath{-}}$ magnetic sub-bands may lead to observable effects in various magneto-optic phenomena in germanium.