Theory of the vertical Hall effect in a dimensionally quantized system

The transverse redistribution of carriers that occurs in a 2D system under the effect of a tangential electric field and a magnetic field possessing a tangential component is studied. It is shown that the redistribution of carriers gives rise to a Hall voltage across isolated electrodes positioned above and under the quantum film. This voltage is determined by the 2D conductivity tensor and the transverse static electric polarizability of the 2D layer. The additional contribution that appears in the vertical Hall voltage because of the electron spin orientation induced by magnetic field and the spin-orbit interaction of electrons with the quantum well potential is determined.