Jerk current: A novel bulk photovoltaic effect

We investigate a physical divergence of the third order polarization susceptibility representing a photoinduced current in biased crystalline insulators. This current grows quadratically with illumination time in the absence of momentum relaxation and saturation; we refer to it as the \textit{jerk current}. Two contributions to the current are identified. The first is a hydrodynamic acceleration of optically injected carriers by the static electric field, and the second is the change in the carrier injection rate in the presence of the static electric field. The jerk current can have a component perpendicular to the static field, a feature not captured by standard hydrodynamic descriptions of carriers in electric fields. We suggest an experiment to detect the jerk current and some of its interesting features.