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]
Review of this, the induced anomalous Hall effect, and other Berry phase-effects on electrons in solid state physics:
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