Shift photocurrent vortices from topological polarization textures

Following the recent interest in van der Waals (vdW) ferroelectrics, topologically nontrivial polar structures have been predicted to form in twisted bilayers. However, these structures have proven difficult to observe experimentally. We propose that these textures may be probed optically by showing that topological polarization textures result in exotic nonlinear optical responses. We derive this relationship analytically using non-Abelian Berry connections and a quantum-geometric framework, supported by tight-binding and first-principles calculations. For the case of moir\'e materials without centrosymmetry, which form networks of polar merons and antimerons, the shift photoconductivity forms a vortex-like structure in real space. For a range of frequencies where transitions between topologically trivial bands occur at the Brillouin zone edge, the shift photocurrents are antiparallel to the in-plane electronic polarization field. Our findings highlight the interplay between complex polarization textures and nonlinear optical responses in vdW materials and provide a sought-after strategy for their experimental detection.