Bulk photovoltaic effects in the presence of a static electric field

This paper presents a study of dc photocurrents in biased insulators to the third order in the electric field. We find three photocurrents which are characterized by physical divergences of the third-order free-electron polarization susceptibility. In the absence of momentum relaxation and saturation effects, these dc photocurrents grow as $t^n$ $(n=2,1,0)$ with illumination time. The photocurrents are dubbed \textit{jerk}, third-order injection, and third-order shift current, respectively, and are generalizations of the second-order injection and shift currents of the bulk photovoltaic effect. We also revisit the theory of the bulk photovoltaic effect and include Fermi surface contributions which are important in metals. Finally, we show that injection, shift, and jerk currents admit simple physical interpretations in terms of semiclassical wave packet dynamics in electric fields. Experimental signatures and extensions to higher-order susceptibilities are also discussed.