We present a framework to calculate the anisotropic and nonlinear photoconductivity for two band systems with application to graphene. In contrast to the usual perturbative (second order in the optical field strength) techniques, we calculate photoconductivity to all orders in the optical field strength. In particular, for graphene, we find the photoresponse to be giant (at large optical field strengths) and anisotropic. The anisotropic photoresponse in graphene is correlated with polarization of the incident field, with the response being similar to that of a half-wave plate. We predict that the anisotropy in the simultaneous measurement of longitudinal (${\sigma }_{xx}$) and transverse $\left({\sigma }_{yx}\right)$ photoconductivity, with four probes, offers a unique experimental signature of the photovoltaic response, distinguishing it from the thermal-Seebeck and bolometric effects in photoresponse.

• Received 6 October 2017

DOI:https://doi.org/10.1103/PhysRevB.97.045402