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Berry phase effects on electronic properties Rev. Mod. Phys. Vol 82, 1959 (2010) Di Xiao, M-C Chang and Qian Niu
Contents (review)
Cyclic adiabatic evolution
Definition of Berry phase
Berry curvature 3D
Berry curvature and Bloch bands
Closed paths in momentum space Two ways An external magnetic field induces cyclotron motion along a closed orbit in q space. An electric field causes linear variation in q. The closed path is completed when the entire Brillouin zone is visited by increasing values of momentum
Parametrization of the Brillouin zone
Berry phase and (name) Hall effect Quantum Hall effect Berry curvature
Anomalous Hall effect Berry curvature
Phonons coupled with magnetic fields Main result: The PHE depends on the Berry curvature
More references PRB 73, (2006) PRB 70, (R) (2004) EPL (2008)