Introducing the concept of anomalous velocity for movement of electron states through the reciprocal space of Bloch momenta in the presence of non-vanishing Berry curvature of the valence bundle:
Ming-Che Chang, Qian Niu: Berry Phase, Hyperorbits, and the Hofstadter Spectrum, Phys. Rev. Lett. 75 (1995) 1348 [doi:10.1103/PhysRevLett.75.1348]
Ming-Che Chang, Qian Niu: Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands, Phys. Rev. B 53 (1996) 7010 [doi:10.1103/PhysRevB.53.7010]
Ganesh Sundaram, Qian Niu: Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Rev. B 59 (1999) 14915 [doi:10.1103/PhysRevB.59.14915]
Review of this, the induced anomalous Hall effect and other Berry phase-effects on electrons in solid state physics:
Di Xiao, Junren Shi, Qian Niu: Berry phase correction to electron density of states in solids, Phys. Rev. Lett. 95 (2005) 137204 [arXiv:cond-mat/0502340, doi:10.1103/PhysRevLett.95.137204]
Di Xiao, Ming-Che Chang, Qian Niu, §III.A in: Berry Phase Effects on Electronic Properties, Rev. Mod. Phys. 82 (2010) 1959-2007 [arXiv:0907.2021, doi:10.1103/RevModPhys.82.1959]
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