Optical probe of Anomalous Hall effect in Weyl semimetals
The Hall effect, discovered in 1879, requires an external magnetic field to produce a transverse (to the applied electric field) electric current in response to the orthogonal configuration of applied magnetic and electric field. The orthgonal setup is also known as Hall effect setup which serves as an essential requisite for the effect. However, not very long ago, it was observed that in certain systems, the Hall effect setup is not required to get Hall effect. This was aptly named as anomalous Hall effect.
In anomalous Hall effect, applied electric field induces current in the perpendicular direction, just like Hall effect but without any magnetic field. The role of magnetic field, in comparision with the original Hall effect, is played by Berry curvature. There are more complicated situations which can give rise to anomalous Hall effect in magnetic systems. However, these origin of anomalous hall effect are dependent on the scattering due to impurity and disorders. In contrast, the the anomalous hall effect originating due to Berry curvature is inherently dependent of the system and not on any external factors. However, what is Berry curvature?
Berry curvature is related to Berry phase. We know that in cyclic adiabatic evolution give rise to dynamical phase factor and Berry phase. Using Stokes' theorem, Berry phase can written as surface integral of the Berry curvature. Hence, Berry curvature is dependent on Hamiltonian and hence wavefunctions alone.