  A single two-dimensional Dirac cone with a mass gap produces a quantized
(spin-) Hall step in the absence of magnetic field. What happens in strong
electric fields? This question is investigated by analyzing time evolution and
dynamics of the (spin-) Hall effect. After switching on a longitudinal electric
field, a stationary Hall current is reached through damped oscillations. The
Hall conductivity remains quantized as long as the electric field (E) is too
weak to induce Landau-Zener transitions, but quantization breaks down for
strong fields and the conductivity decreases as 1/sqrt{E}. These apply to the
(spin-) Hall conductivity of graphene and the Hall and magnetoelectric response
of topological insulators.
