magnetic field driven 2D spin-orbit coupled system

We consider a two-dimensional spin-orbit coupled system subjected to an in-plane magnetic field, which can be realized in the Rashba spin-orbit coupled system or the surface state of a topological insulator. Although the static Zeeman magnetic field does not induce an electric current, a time-dependent one can induce such a current in the direction perpendicular to the Zeeman field. Since the spin-orbit coupling can be viewed as a consequence of an electric field perpendicular to the 2D plane, the electric field, the magnetic field, and the response current form a triad, which is different from the Hall effect in which the magnetic field is out of plane while the electric field is in plane.