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

Abstract

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 2π 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.