Geometric phases and time-odd coupling in Jahn-Teller systems

Time-odd (momentum) coupling between the nuclear and electronic wavefunctions in Jahn-Teller systems, although smaller than the traditional time-even (electrostatic) coupling terms, can dramatically change the geometric phase. In the cubic E ⊗ ε system, whose geometrical phase is a multiple of π, time-odd coupling of modes with A₂a symmetry gives a three-dimensional parameter space and arbitrary geometrical phases. We show that for equal coupling the geometric vector potential takes the form of a monopole and hence that (as in the time-even case) the nuclear angular momentum for the system is shifted from integer to half-integer values.