Symmetry properties of the direct nonparabolic L-excitons in semiconductors of the T2d (F4̄3m) space group and vector-coupling coefficients for CdTe

In most III–V and II–VI compounds with the $\text{F}\text{4}\text{̄}\text{3}\text{m}$ zinc-blende structure, such as GaAs, CdTe, InP, and also in fcc alkali halides and solid Xenon, the experimental reflectivity peaks near the first Λ and L-transitions are enhanced and probably caused by excitons. In CdTe the reflectivity drops sharply at 3.46 and 4.03 eV and this is to be associated with the electron-hole bound state at the L point and the near by Λ symmetry line. The total symmetry of L and Λ excitons are fully determined by the irreducible representations contained in L₆×L_4,5 and Λ₆×Λ_4,5, and these follow from momentum conservation and selection rules. We have determined the allowed L and Λ exciton momenta. The proper exciton wave function symmetries needed in the variational method for exciton binding energies have been determined by Vector-Coupling Coefficients (VCCs), (known also as the Clebsch–Gordan Coefficients (CGCs)), for the direct non parabolic excitons of the L₆×L_4,5 symmetry. The CGCs can be helpful in the evaluation of intensity of optical transitions, Raman scattering tensors and effective Hamiltonians.