Berry’s phase for energy bands in solids

1989/06/05 by J. Žák · 1 voice · 128 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Mechanical and Optical Resonators #Photorefractive and Nonlinear Optics

paper · doi:10.1103/physrevlett.62.2747

openalex publication_date 1989/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

Berry's phase is defined for the dynamics of electrons in periodic solids and an explicit formula is derived for it. Because of the special torus topology of the Brillouin zone a nonzero Berry phase is shown to exist in a one-dimensional parameter space. Symmetry of the Bloch functions in the Brillouin zone leads to the quantization of Berry's phase. A connection is established between the latter and the Wyckoff positions in the crystal in the framework of band representations of space groups. Berry's phase can therefore be used for labeling energy bands in solids.

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Discussions

• In the presence of inversion symmetry, the Zak phase is quantized to integers of $\pi$ (modulo $2\pi$ ) (see Zak's paper ( PDF )). The Zak for the $n^{th}$ band is given by $$ Z_n = i\int_{-\pi}^\pi d [stackexchange, 1 points]

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