Unified First-Principles Theory of Finite-Wave-Vector Photocurrents in Crystals

Abstract

Spatially structured light carries independent phase and envelope variations in addition to its polarization and frequency. We develop a first-principles theory of second-order dc photocurrents (especially shift and injection) that resolves how these optical degrees of freedom drive distinct dc responses in crystals. The second-order dc response couples two optical field components at the same frequency but with generally different wave vectors. Expanding the response to first order in these wave vectors identifies two rank-four material tensors: $ξ$, which couples to the optical phase gradient and contains the plane-wave photon-drag limit, and $ζ$, which couples to the intensity gradient and describes a spatially varying dc current. Wannier-interpolated calculations for monolayer GeS show symmetry-allowed finite-wave-vector responses that survive at a centrosymmetric structure where conventional bulk photovoltaic effect vanishes. For a Gaussian beam with a uniform phase gradient, the phase-gradient contribution drives current in the same direction on both sides of the beam center, whereas the intensity-gradient contribution drives currents in opposite directions, showing that distinct photocurrent patterns can be selected through the wavefront and envelope of light. A multipolar analysis further resolves the optical corrections into electric-quadrupole, orbital magnetic-dipole, and band-dispersion contributions. Together, these results show how the spatial structure of light can serve as an independent control variable for nonlinear photocurrent generation and provide a first-principles route to predict this response in real materials.