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)