Opto-twistronic Hall effect in a three-dimensional spiral lattice

Studies of moire systems have elucidated the exquisite effect of quantum geometry on the electronic bands and their properties, leading to the discovery of new correlated phases. However, most experimental studies have been confined to a few layers in the 2D limit. The extension of twistronics to its 3D limit, where the twist is extended into the third dimension between adjacent layers, remains underexplored due to the challenges in precisely stacking layers. Here, we focus on 3D twistronics on a platform of self-assembled spiral superlattice of multilayered WS2. Our findings reveal an opto-twistronic Hall effect in the spiral superlattice. This mesoscopic response is an experimental manifestation of the noncommutative geometry that arises when translational symmetry is replaced by a non-symmorphic screw operation. We also discover signatures of altered laws of optical excitation, manifested as an unconventional photon momentum-lattice interaction owing to moire of moire modulations in the 3D twistronic system. Crucially, our findings mark the initial identification of higher-order quantum geometrical tensors in light-matter interactions. This breakthrough opens new avenues for designing quantum materials-based optical lattices with large nonlinearities, paving the way for the development of advanced quantum nanophotonic devices.