Dynamical Jahn-Teller Effect and Berry Phase in Positively Charged Fullerene I. Basic Considerations

TL;DR

This paper investigates the Jahn-Teller effect and Berry phase in positively charged fullerene ions, revealing the conditions under which a Berry phase appears and its implications for molecular symmetry and excitations.

Contribution

It provides a theoretical analysis of the Berry phase in positive fullerene ions, extending understanding of Jahn-Teller effects and their quantum consequences in these molecules.

Findings

No Berry phase in $^1$C$_{60}^{2+}$

Berry phase depends on coupling of hole to vibrations

Special equal-coupling case reduces to particle on a 5D sphere

Abstract

We study the Jahn-Teller effect of positive fullerene ions $^2$C$_{60}^{+}$ and $^1$C$_{60}^{2+}$. The aim is to discover if this case, in analogy with the negative ion, possesses a Berry phase or not, and what are the consequences on dynamical Jahn-Teller quantization. Working in the linear and spherical approximation, we find no Berry phase in $^1$C$_{60}^{2+}$, and presence/absence of Berry phase for coupling of one $L=2$ hole to an $L=4$/$L=2$ vibration. We study in particular the special equal-coupling case ($g_2=g_4$), which is reduced to the motion of a particle on a 5-dimensional sphere. In the icosahedral molecule, the final outcome assesses the presence/absence of a Berry phase of $\pi$ for the $h_u$ hole coupled to $G_g$/$H_h$ vibrations. Some qualitative consequences on ground-state symmetry, low-lying excitations, and electron emission from C$_{60}$ are spelled out.