Electron--Vibron Interactions and Berry Phases in Charged Buckminsterfullerene: Part I

TL;DR

This paper models electron-vibron interactions in charged buckminsterfullerene, revealing how Jahn-Teller distortions and Berry phases influence ground states and pairing energies, with implications for superconductivity in fullerides.

Contribution

It introduces a unified model analyzing electron-vibron interactions at both weak and strong couplings, highlighting the role of Berry phases and Jahn-Teller effects in fullerene.

Findings

Jahn-Teller distortions are unimodal for n=1,2,4,5 and bimodal for n=3.

Berry phases cause ground state degeneracies and alter zero point energies.

Pair binding energies are enhanced by a factor of 5/2 over classical estimates.

Abstract

A simple model for electron-vibron interactions on charged buckminsterfullerene C$_{60}^{n-}$, $n=1,\ldots 5$, is solved both at weak and strong couplings. We consider a single $H_g$ vibrational multiplet interacting with $t_{1u}$ 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 pseudo--rotators 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.