Exciton states of semiconductors in a high magnetic field

Exciton states of diamond and zinc-blende semiconductors in a high magnetic field are investigated taking into full account the degeneracy and anisotropy of the valence bands. An improved version of the adiabatic method introduced by Rees is derived and generalized for arbitrary orientation of the field. Simple one-dimensional adiabatic Hamiltonians which describe the motion component parallel to the magnetic field are obtained. The introduction of a suitable set of Gaussian basis functions is shown to provide exact analytical expressions for the adiabatic-potentials matrix elements. A very accurate procedure is used to diagonalize the Hamiltonians for the various states. Results are obtained for $\overrightarrow{H}$ parallel to the [001] and [110] directions and for several materials. The range of validity of the present adiabatic approach is discussed, and the theoretical results are compared to experiment.