In reference to the recent Science article, "The valley Hall Effect in MoS2" there is a Hall voltage developed when monolayer MoS2 is illuminated by circularly polarized light. There are no external sources of magnetic field in this experiment and yet there is a hall voltage.
http://www.sciencemag.org/content/344/6191/1489.abstract
to describe on the type of carries of charge, the mobility and the concentration of charge carriers
Just like spin Hall effect, no external magnetic field is required. "Internal" valley magnetization of MoS2 is nonzero because of broken inversion symmetry and it can manifest anomalous Hall effect (separation of K and K' valley electrons in this case) when an in-plane potential difference is applied.
Its basically like the motion of the electrons induced a magnetic-like field( the Berry curvature), and electrons/holes feels a force in this field which caused them move to the edges. There is a RMP paper Berry phase effects on electronic properties, I think it will serve you well.
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