title: Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation.
abstract: We have measured optical second-harmonic generation (SHG) from atomically thin samples of MoS2 and h-BN with one to five layers. We observe strong SHG from materials with odd layer thickness, for which a noncentrosymmetric structure is expected, while the centrosymmetric materials with even layer thickness do not yield appreciable SHG. SHG for materials with odd layer thickness was measured as a function of crystal orientation. This dependence reveals the rotational symmetry of the lattice and is shown to provide a purely optical method of determining the orientation of crystallographic axes. We report values for the nonlinearity of monolayers and odd-layers of MoS2 and h-BN and compare the variation as a function of layer thickness with a model that accounts for wave propagation effects.
authors.affiliation: Departments of Physics and Electrical Engineering, Columbia University , 538 West 120th Street, New York, New York 10027, United States.
authors.forename: Yilei
authors.initials: Y
authors.lastname: Li
authors.forename: Yi
authors.initials: Y
authors.lastname: Rao
authors.forename: Kin Fai
authors.initials: KF
authors.lastname: Mak
authors.forename: Yumeng
authors.initials: Y
authors.lastname: You
authors.forename: Shuyuan
authors.initials: S
authors.lastname: Wang
authors.forename: Cory R
authors.initials: CR
authors.lastname: Dean
authors.forename: Tony F
authors.initials: TF
authors.lastname: Heinz