Berry’s phase for energy bands in solids

1989/06/05 by J. Žák · 1 voice · 18 citations
Physics and Astronomy · #Photorefractive and Nonlinear Optics #Mechanical and Optical Resonators #Advanced Chemical Physics Studies

paper · doi:10.1103/physrevlett.62.2747

openalex publication_date 1989/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

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.

Cited by

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• Realizing the Haldane Model in Thermal Atoms
• Topological Localisation in Time from PT Symmetry
• Metamaterials and Fluid Flows
• Topological edge states in a double isomeric Class-II oligo(indenoindene)
• Localized heat diffusion in topological thermal materials
• Nonadiabatic Wave-Packet Dynamics: Nonadiabatic Metric, Quantum Geometry, and Gravitational Analogy
• Charge current and phase diagram of the disordered open longer-range Kitaev chain
• High-root topological edge-state bands
• Topology in Holographic Mean-Field Theory at Zero and Finite Temperature
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Non-periodic Boundary Conditions for Euler Class and Dynamical Signatures of Obstruction
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Electric-field control of two-dimensional ferromagnetic properties by chiral ionic gating

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]

Related

• Berry phase effects on electronic properties
• Berry's Phase for Ultracold Atoms in an Accelerated Optical Lattice
• A formally exact real-space representation of the Berry phase on infinite lattices: Applications to dipole and quadrupole moments
• Zak's Phase in Non-Symmetric One-Dimensional Crystals
• Some geometric features of Berry's phase