Hall effect in an AC electric field and related phenomena

Nonlinear Hall effect in an AC electric field and related phenomena. Abstract It has been shown that in metals and semiconductors the joint action of permanent magnetic and AC electric fields leads to arising of DC surface electric current. The physical reason for such a current is due to essentially non-linear dynamics of electronic gas in the surface layer. In adiabatic limit the analytical expression for the current are given. Two cases have been considered: a surface current inside metal at the metal-insulator boundary and a current in an injection layer on metal-semiconductor boundary. General equations of electronic gas dynamics have been solved numerically. The surface current is linear with respect to magnetic field and depends quadratically on an amplitude of external AC electric field. In inhomogeneous media with non-zero gradient of conductivity there can be the bulk current. Corresponding phenomenological expression is obtained.The conditions for spontaneous generation of magnetic field have been found. The directed transport of particles under action of AC driving force is now well established phenomenon in various non-linear systems. Most detailed this transport has been studied for one-dimensional motion of particle in the space-periodic potential U(x) and a time-periodic force having general form F (t) = F 0 cos ωt + F 1 cos (2ωt + θ). (See review [1] and recent works [2, 3, 4].) Main physical reason for the directed motion of the particles is connected with the so called latent asymmetry of driving force F (t). Though the time average of F (t) is zero the time average F 3 (t) doesn't vanish and depends on θ. Non-linearity of the system with potential U(x) leads to mixing of harmonics such a way that average velocity is not zero and directed along F 3 (t) .The necessary symmetry conditions for U(x) and F (t) are considered in [4].