Title: Twisted nonlinear optics in monolayer van der Waals crystals

Abstract: In addition to a plethora of emergent phenomena, the spatial topology of optical vortices enables an array of applications spanning communications to quantum photonics. Nonlinear optics is essential in this context, providing access to an infinitely large set of quantum states associated with the orbital angular momentum of light. Nevertheless, the realization of such processes have failed to keep pace with the ever-growing need to shrink the fundamental length-scale of photonic technologies to the nanometer regime6. Here, we push the boundaries of vortex nonlinear optics to the ultimate limits of material dimensionality. By exploiting second and third-order frequency-mixing processes in semiconducting monolayers, we demonstrate the independent manipulation of the wavelength, orbital angular momentum, and spatial distribution of vortex light-fields. Due to the atomically-thin nature of the host quantum material, this control spans a broad spectral bandwidth in a highly-integrable platform, unconstrained by the traditional limits of bulk nonlinear optical materials. Our work heralds a new avenue for ultra-compact and scalable hybrid nanotechnologies empowered by twisted nonlinear light-matter interactions in van der Waals quantum nanomaterials.