Scattering matrix for two phonon processes at k = 0 in Si and Ge of O(sup7)(subh) symmetry is given. Also diagonalization of spin-orbit interaction Hamiltonian has been computed by means of Clebsh-Gordan coefficients. The authors have concluded that they have used group theoretical method for diagonalization of two-phonon using symmetrized Kronecker product. They also have diagonalized SO matrices. Their method can be extended to three-phonon processes as well as to other interactions like spin-spin, inter- and intravalley scattering. Their results are valid for all compounds with O(sup7(subh) symmetry.
Reference:
Kunert, HW, Machatine, AGJ, Niyongabo, P, Govender, M and Mwakikunga, BW. 2013. Clebsch-Gordan coefficients for scattering processes in Si and Ge. Physica Status Solidi C, vol. 9(10-11), pp 1978–1980
Kunert, H., Machatine, A., Niyongabo, P., Govender, M., & Mwakikunga, B. W. (2012). Clebsch-Gordan coefficients for scattering processes in Si and Ge. http://hdl.handle.net/10204/7063
Kunert, HW, AGJ Machatine, P Niyongabo, M Govender, and Bonex W Mwakikunga "Clebsch-Gordan coefficients for scattering processes in Si and Ge." (2012) http://hdl.handle.net/10204/7063
Kunert H, Machatine A, Niyongabo P, Govender M, Mwakikunga BW. Clebsch-Gordan coefficients for scattering processes in Si and Ge. 2012; http://hdl.handle.net/10204/7063.
