Dynamical Jahn-Teller effect and Berry phase in positively charged fullerenes: Basic considerations.

We study the Jahn-Teller effect of positive fullerene ions {sup 2}C{sub 60}{sup +} and {sup 1}C{sub 60}{sup 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 {sup 1}C{sub 60}{sup 2+}, and presence/absence of Berry phase for coupling of one {ital L}=2 hole to an {ital L}=4/{ital L}=2 vibration. We study in particular the special equal-coupling case ({ital g}{sub 2}={ital g}{sub 4}), which is reduced to the motion of a particle on a five-dimensional sphere. In the icosahedral molecule, the final outcome assesses the presence and/or absence of a Berry phase of {pi} for the {ital h}{sub {ital u}} hole coupled to {ital G}{sub {ital g}}/{ital H}{sub {ital h}} vibrations. Some qualitative consequences on ground- state symmetry, low-lying excitations, and electron emission from C{sub 60} are spelled out. {copyright} {ital 1996 The American Physical Society.}