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 deff ~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 deff = 0.77 nm/V for monolayer WS2, which shows good order-of-magnitude agreement with the experimental result.
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