Berry’s geometrical phase and the sequence of states in the Jahn-Teller effect

A proof is given for the Jahn-Teller problem of an orbital doublet (E{}{ε}) that the order of the lowest vibronic levels is fixed by the requirement that the vibrational part of the wave function change sign under 2{π} rotation in the vibrational coordinates. This sign change in turn is a consequence of the sign change in the electronic part of the wave function, a special case of Berry's geometrical phase. Experimental confirmation of this sign change and thus of Berry's phase is available from studies of Jahn-Teller defects in crystals that reveal the sequence of these lowest levels.