Berry’s phase in the effective-Hamiltonian theory of solids

The appearance of Berry’s phase in the effective-Hamiltonian theory for the impurity problem in semiconductors is investigated. An analogy is drawn between the Born-Oppenheimer approximation in molecular spectra and the one-band approximation in the impurity problem. The kq representation is used to show that in the latter problem the quasicoordinate q and the quasimomentum k for the electron (k and q are parts of the single coordinate r of the electron) replace the coordinates r of the electrons and R of the nuclei, correspondingly. Based on this analogy and the recent experimental observation of Berry’s-phase influence on the molecular spectrum, attention is drawn to the possibility of the observation of a similar effect in the spectrum of shallow impurities in semiconductors.