The relativistic E × E Jahn-Teller effect revisited

The vibronic Hamiltonian describing linear Jahn-Teller coupling as well as spin-orbit coupling in systems of trigonal symmetry is derived in the diabatic spin-orbital representation, employing the microscopic (Breit-Pauli) spin-orbit coupling operator in the single-electron approximation. The analysis generalizes previous treatments based on more phenomenological models of spin-orbit coupling. It is shown that an alternative time-reversal symmetry adapted diabatic representation exists, in which the 4 × 4 Jahn-Teller spin-orbit vibronic Hamiltonian is block-diagonal. The adiabatic electronic wave functions are obtained in explicit form. The topological phases (Berry's phases) of all four adiabatic electronic basis states are calculated. As found previously for the special case of systems with D3h symmetry, the topological phases depend on the radius of the loop of integration.