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Using group theoretical techniques we have investigated all single valued representations as well as double valued, these follow from the inclusion of spin, of wurtzite space groups, respectively, with regard to the presence or absence of Time Reversal Symmerty (TRS). We have found a number of phonons in wurtzite and trigonal structures to be time reversal degenerate, whereas in the cubic Si, Ge and diamond the vibrational modes are not time reversal degenerate. Electronic band structure also experience extra TRS degeneracy. Therefore, the selections rules for optical radiative transitions need modification.

Phonons and electronic states of ZnO, Al2O3and Ge in the presence of time reversal symmetry

Phonons and electronic states of ZnO, Al₂O₃and Ge in the presence of time reversal symmetry