Analysis of a two dimensional molecular Berry phase system

Abstract

Discontinuities in the Born–Oppenheimer (infinite nuclear masses) limit of an artificial molecular system, absent for finite masses, have led Min et al. (2014) to a questioning of Berry phases in some molecular systems. We show here by a rigorous following of the analysis of Longuet-Higgins et al. (1958), that (a) the same phenomena of discontinuities occurs in typical degenerate molecular systems with regular Berry-phase effects, (b) they arise from the non-unique definition of the key quantity, electronic ‘vector field’, and (c) they can be removed by a different choice of normalization.