Berry phase and the Gamma 8

Abstract

The ground-state Berry phase of the ${\mathrm{\ensuremath{\Gamma}}}_{8}$\ensuremath{\bigotimes}(${\mathrm{\ensuremath{\tau}}}_{2}$\ensuremath{\bigoplus}\ensuremath{\epsilon}) Jahn-Teller system in strong coupling is calculated, for both equal and unequal couplings to the phonon modes. Because of time-reversal invariance and the resulting degeneracy in the states, the usual Berry-phase analysis for the time evolution of nondegenerate states must be augmented by the generalized formalism of Wilczek and Zee. In the ${\mathrm{\ensuremath{\Gamma}}}_{8}$\ensuremath{\bigotimes}(${\mathrm{\ensuremath{\tau}}}_{2}$\ensuremath{\bigoplus}\ensuremath{\epsilon}) system, the Berry-phase factor becomes a 2\ifmmode\times\else\texttimes\fi{}2 unitary matrix. Explicit analytical expressions for the ground states are derived.