Configurational Instability in Solids: Diamond and Zinc Blende

The Jahn-Teller theorem, which has been established by enumeration for the 32 point groups and the icosahedral groups, is extended to two space groups: diamond ${O_h}^7$ and zinc blende ${T_d}^2$. We show that almost all degenerate electronic states in these structures give rise to configurational instability, that is to forces tending to distort the space group to one of lower symmetry and concomitantly to split the degeneracy. Not only the degeneracy due to the touching of energy surfaces, but also the star degeneracy can be wholly or in part lifted. We believe this theorem will apply to all the space groups, but each space group must be individually examined. Some qualitative, illustrative, applications of the theorem to exciton splittings in diamond and zinc blende are given. Possible applications are mentioned, for other space groups.