Bulk photovoltaic effects in the presence of a static electric field

Irradiated crystalline insulators in the presence of a static electric field exhibit three new types of nonlinear photocurrents. They represent physical singularities of the third order free electron polarization susceptibility and hence generalize the standard second order bulk photovoltaic effects. In the absence of momentum relaxation and saturation effects they grow as $t^n$ $(n=2,1,0)$ with illumination time and are dubbed \textit{jerk}, \textit{modified injection}, and \textit{modified shift} current, respectively. The presence of a static electric field gives rise to new processes which are described in detail. Experimental signatures and extensions to higher order susceptibilities are also discussed.