title: Extraordinary Second Harmonic Generation in tungsten disulfide monolayers.
abstract: 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.
authors.affiliation: 1] Department of Electrical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802 [2] Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802.
authors.forename: Corey
authors.initials: C
authors.lastname: Janisch
authors.affiliation: 1] Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802 [2] Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802.
authors.forename: Yuanxi
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Department of Electrical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802.
authors.forename: Ding
authors.initials: D
authors.lastname: Ma
authors.affiliation: Department of Electrical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802.
authors.forename: Nikhil
authors.initials: N
authors.lastname: Mehta
authors.affiliation: 1] Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802 [2] Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802.
authors.forename: Ana Laura
authors.initials: AL
authors.lastname: Elías
authors.affiliation: 1] Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802 [2] Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802.
authors.forename: Néstor
authors.initials: N
authors.lastname: Perea-López
authors.affiliation: 1] Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802 [2] Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802 [3] Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802 [4] Department of Materials Science & Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802.
authors.forename: Mauricio
authors.initials: M
authors.lastname: Terrones
authors.affiliation: 1] Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802 [2] Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802 [3] Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802 [4] Department of Materials Science & Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802.
authors.forename: Vincent
authors.initials: V
authors.lastname: Crespi
authors.affiliation: 1] Department of Electrical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802 [2] Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802.
authors.forename: Zhiwen
authors.initials: Z
authors.lastname: Liu