Shift of Landau Levels in the Valence Band of Germanium in Crossed Electric and Magnetic Fields

Optical-absorption and Voigt-effect measurements in germanium have been performed in crossed electric and magnetic fields for photon energies just below the direct gap. The electric fields were taken between 2.8×{}10⁴ and 4.7×{}10⁴ V/cm, the magnetic fields were chosen between 62.5 and 96.5 kOe. Three transitions were observed, two of which are allowed for E=0 (Δn=0), whereas the third is forbidden for $E=0$, but is induced by the electric field (Δn=-1). From the experimental data the energies of the three light-hole levels $|0a+〉$, $|1a+〉$, and $|0b+〉$ are deduced, under the assumption that the energies of the electron levels can be calculated according to the theory for a simple parabolic band in cross fields. A calculation is developed for the energies of the light-hole levels in cross fields for the range of high (E/H) values where a perturbation treatment is not sufficient. This calculation is within the framework of the effective-mass approximation and neglects the electric-field-induced coupling between light- and heavy-hole states. The theory shows that for higher (E/H) values the electric-field-induced shifts of the light-hole levels are comparable to those that would have been found in simple bands, and that the electric field removes the quantum effects in the energies of the light-hole levels. The theory is in satisfactory agreement with the experimental results.