Ultrathin 3R-MoS$_2$ metasurfaces with atomically precise edges for efficient nonlinear nanophotonics

Dielectric metasurfaces that combine high-index materials with optical nonlinearities are widely recognized for their potential in various quantum and classical nanophotonic applications. However, the fabrication of high-quality metasurfaces poses significant material-dependent challenges, as their designs are often susceptible to disorder, defects, and scattering losses, which are particularly prone to occur at the edges of nanostructured features. Additionally, the choice of the material platforms featuring second-order optical nonlinearities, $\chi^{(2)}$, is limited to broken-inversion symmetry crystals such as GaAs, GaP, LiNbO$_3$, and various bulk van der Waals materials, including GaSe and NbOCl$_2$. Here, we use a combination of top-down lithography and anisotropic wet etching of a specially stacked van der Waals crystal -- 3R-MoS$_2$, which exhibits both a high refractive index and exceptional $\chi^{(2)}$ nonlinearity, to produce metasurfaces consisting of perfect equilateral triangle nanoholes with atomically precise zigzag edges. Due to the geometry of the triangle, the etching process is accompanied by a transition from an in-plane $C_4$ symmetric structure to a broken-in-plane symmetry configuration, thereby allowing for the realization of the quasi-bound-state-in-the-continuum (q-BIC) concept. The resulting ultrathin metasurface ($\sim$ 20-25 nm) demonstrates a remarkable enhancement in second-harmonic generation (SHG) -- over three orders of magnitude at specific wavelengths and linear polarization directions compared to a host flake.