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

The energies of the magnetic sub-bands associated with the V₁ and V₂ valence bands in germanium have been calculated as a function of kz, the propagation constant parallel to the external magnetic field. Warping of the V₁ and V₂ bands was neglected. Sub-bands belonging to the 1⁺ and 2⁺ ladders (light holes) have minima at kz=0 and show quantum effects consisting of a decrease in curvature as the valence band edge is approached. Sub-bands belonging to the 2^- ladder (heavy holes) also have minima at kz=0, but the curvatures increase near the valence band edge. The 1^- heavy hole sub-bands show very marked quantum effects. The sub-band minima occur at values of kz different from zero, and local maxima appear at kz=0. The peculiar nature of the 1^- magnetic sub-bands may lead to observable effects in various magneto-optic phenomena in germanium.