Extraordinary Second Harmonic Generation in tungsten disulfide monolayers.

We investigate Second Harmonic Generation (SHG) in monolayer WS₂ both deposited on a SiO₂/Si substrate or suspended using transmission electron microscopy grids. We find unusually large second order nonlinear susceptibility, with an estimated value of d(eff) ~ 4.5 nm/V nearly three orders of magnitude larger than other common nonlinear crystals. In order to quantitatively characterize the nonlinear susceptibility of two-dimensional (2D) materials, we have developed a formalism to model SHG based on the Green's function with a 2D nonlinear sheet source. In addition, polarized SHG is demonstrated as a useful method to probe the structural symmetry and crystal orientation of 2D materials. To understand the large second order nonlinear susceptibility of monolayer WS₂, density functional theory based calculation is performed. Our analysis suggests the origin of the large nonlinear susceptibility in resonance enhancement and a large joint density of states, and yields an estimate of the nonlinear susceptibility value d(eff) = 0.77 nm/V for monolayer WS₂, which shows good order-of-magnitude agreement with the experimental result.