Electron-vibron interactions in charged fullerenes. I. Berry phases

A simple model for electron-vibron interactions on charged fullerenes ${\mathrm{C}}_{60}^{\mathit{n}\mathrm{-}}$, n=1,...,5, is solved both at weak and strong couplings. We consider a single ${\mathit{H}}_{\mathit{g}}$ vibrational multiplet interacting with ${\mathit{t}}_{1\mathit{u}}$ electrons. At strong coupling the semiclassical dynamical Jahn-Teller theory is valid. The Jahn-Teller distortions are unimodal for n=1,2,4,5 electrons, and bimodal for 3 electrons. The distortions are quantized as rigid-body pseudorotators which are subject to geometrical Berry phases. These impose ground-state degeneracies and dramatically change zero-point energies. Exact diagonalization shows that the semiclassical level degeneracies and ordering survive well into the weak-coupling regime. At weak coupling, we discover an enhancement factor of 5/2 for the pair binding energies over their classical values. This has potentially important implications for superconductivity in fullerides, and demonstrates the shortcoming of Migdal-Eliashberg theory for molecular crystals.