Relevance of multiband Jahn-Teller effects on the electron-phonon interaction in A3C60

Assessing the effective relevance of multiband effects in fullerides is of fundamental importance in understandingthe complex properties of these compounds. In this paper we investigate the role of the multibandeffects on the electron-phonon el-ph properties of the t1u bands coupled with the Jahn-Teller intramolecularHg vibrational modes in C60 compounds. We show that, assuming perfect degeneracy of the electronic bands,vertex diagrams arising from the breakdown of the adiabatic hypothesis, are one order of magnitude smallerthan the noncrossing terms usually retained in the Migdal-Eliashberg ME theory. These results permit tounderstand the robustness of the ME theory found by numerical calculations. The effects of the nondegeneracyof the t1u in realistic systems are also analyzed. Using a tight-binding model we show that the el-ph interactionis mainly dominated by intraband scattering within a single electronic band. Our results question the reliabilityof a degenerate band modeling and show the importance of these combined effects in the A3C60 family.