Seria interessante iniciar uma linha de pesquisa sobre fases geométrica em sistemas de estado sólido? 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)

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# PPT - l. Sanz