Theory of exciton effects in the high-field magnetoabsorption of real semiconductors

Direct exciton states of cubic semiconductors in a high magnetic field are investigated taking into full account the degeneracy and anisotropy of the valence bands. The adiabatic method is used to decouple the components of the motion parallel and perpendicular to the magnetic field. One-dimensional Hamiltonians are obtained analytically for the various exciton states and selection rules for optical transitions are discussed. Accurate numerical values of the energy levels are given for H parallel to the (110) direction. The results obtained provide the first quantitative interpretation of the fine structure observed in high resolution measurements of magnetoabsorption in Ge.