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

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^{-}

ladder (heavy holes) also have minima at

k_{z} = 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

k_{z}

different from zero, and local maxima appear at

k_{z} = 0

. The peculiar nature of the

1^{-}

magnetic sub-bands may lead to observable effects in various magneto-optic phenomena in germanium.

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