Vibrations and Berry phases of charged buckminsterfullerene

A simple model of electron-vibron interactions in buckminsterfullerene ions is solved semiclassically. Electronic degeneracies of ${\mathrm{C}}_{60}^{\mathit{n}\mathrm{-}}$ induce dynamical Jahn-Teller distortions, which are unimodal for n≠3 and bimodal for n=3. The quantization of motion along the Jahn-Teller manifold leads to a symmetric-top rotator Hamiltonian. I find molecular Aharonov-Bohm effects where electronic Berry phases determine the vibrational spectra, zero point fluctuations, and electrons’ pair binding energies. The latter are relevant to superconductivity in alkali fullerenes.