Non-Ohmic critical fluctuation Hall conductivity of layered   superconductors in strong electric fields
  The excess Hall conductivity, resulting from thermal fluctuations of the superconducting order parameter, is calculated for a layered superconductor for an arbitrarily strong in-plane electric field and a perpendicular magnetic field in the frame of the time-dependent Ginzburg-Landau theory. The fluctuation Hall conductivity is suppressed in high electric fields much stronger than the longitudinal one. For high-temperature superconductors we predict a pronounced non-Ohmic behavior of the excess Hall effect near the critical temperature in moderate magnetic fields and electric fields of the order of 100 V/cm. 
I. Puica, W. Lang