Phonons in the beta-tin, Imma, and sh phases of Silicon from ab initio calculations

We study the lattice statics and dynamics of Si near the beta-tin->Imma->sh phase transitions. The pressure at and the order of the phase transitions can be determined precisely from the dynamical rather than the static properties. We also present a new interpretation of measured Raman frequencies of a high-pressure structure of Silicon correcting a previous assignment to the beta-tin phase, since the Imma phase was unknown. With the new assignment, the ab initio phonon frequencies display an excellent agreement with the experimental data. The sh->Imma transition is accompanied by soft modes which should be accessible in future experiments. The phonon-dispersion curves and density of states point at irregularities of the behavior of the superconducting temperature as a function of the pressure for these phases.