Anomalous Hall effect for semiclassical chiral fermions

• Chiral fermions exhibit an anomalous spin-Hall effect.
• Transverse shift appears in a pure electric field.
• In a pure magnetic field spiraling motion is found.

Semiclassical chiral fermions manifest the anomalous spin-Hall effect: when put into a pure electric field they suffer a side jump, analogous to what happens to their massive counterparts in non-commutative mechanics. The transverse shift is consistent with the conservation of the angular momentum. In a pure magnetic field, instead, spiraling motion is found. Motion in Hall-type perpendicular electric and magnetic fields is also studied.