Non-linear Photocurrent from First-principles Real-time Density Matrix Dynamics

The photogalvanic effect (PGE) is a second-order phenomenon where non-centrosymmetric materials generate a steady direct current (DC) under illumination. In this work, we develop a fully first-principles quantum kinetic theory based on density matrix formalism to describe nonlinear photocurrent, applicable for both transient and steady states. Unlike past perturbative approaches, we include complete kinetic processes including excitation, quantum scatterings, and stimulated and spontaneous recombinations, where we obtain the shift current and injection current from a unified framework. In particular, we found electron-phonon scatterings induce large shift current through phonon-mediated intra-band relaxation, nearly the same order as the excitation shift current. We benchmarked our methodology through a prototypical example BaTiO₃ and found good agreement with experimental results, in particular providing an explanation of past work's underestimation through phonon shift current. Our study offers a comprehensive understanding of nonlinear photocurrent mechanisms and provides a general framework for investigating a range of nonlinear optical effects.