Quadrupolar bulk photovoltaic effect in centrosymmetric crystals enhanced by quantum geometry

The bulk photovoltaic effect is a coherent quantum mechanism for generating photocurrents in a homogenous crystal that has attracted interest both as a probe of band geometry and as a platform for next-generation optoelectronics. While previous work has primarily focused on photocurrents arising from spatially uniform optical excitation, which requires an inversion-breaking crystal, here we extend beyond the dipole approximation and consider the photocurrent response of a centrosymmetric crystal to a gradient in light intensity (i.e. at first order in the wavevector of the light). We identify two distinct purely quantum-geometric contributions stemming from virtual transitions mediated by electric quadrupole matrix elements in addition to ordinary dipole transitions, which may dominate the response in centrosymmetric systems with geometrically nontrivial band structure. Our work elucidates a fundamentally quantum-geometric mechanism for the breakdown of the dipole approximation in solid-state systems, revealing design principles for realizing centrosymmetric bulk photovoltaics in experiment.