The Berry phase rectification tensor and the solar rectification vector
We introduce an operational definition of the Berry Phase Rectification Tensor as the second order change of polarization of a material in response to an ideal short pulse of electric field. Under time reversal symmetry this tensor depends exclusively on the Berry phases of the Bloch bands and not on their energy dispersions, making it an intrinsic property to each material which contains contributions from both the inter-band shift currents and the intra-band Berry Curvature Dipole. We also introduce the Solar Rectification Vector as a technologically relevant figure of merit for bulk photo-current generation which counts the number of electrons contributing to the rectified current per incoming photon under ideal black-body radiation in analogy with the classic solar cell model of Shockley and Queisser. We perform first principle calculations of the Berry Phase Rectification Tensor and the Solar Rectification Vector for the Weyl semi-metal TaAs and the insulator LiAsSe2 which features large shift currents close to the peak of solar radiation intensity. We also generalize the formula for the Glass coefficient to include the spectral distribution of the incoming radiation, the directionality dependence of the conductivity of the material and the reflectivity at its surface.