Seria interessante iniciar uma linha de
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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)
Contents (review)
Cyclic adiabatic evolution
Definition of Berry phase
Berry curvature
3D
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, 125330 (2006)
• PRB 70, 081311(R) (2004)
• EPL 82 60006 (2008)