The translational symmetry breaking of a crystal at its surface may form two-dimensional (2D) electronic states. We observed one-dimensional nonlinear optical edge states of a single atomic membrane of molybdenum disulfide (MoS 2 ), a transition metal dichalcogenide. The electronic structure changes at the edges of the 2D crystal result in strong resonant nonlinear optical susceptibilities, allowing direct optical imaging of the atomic edges and boundaries of a 2D material. Using the symmetry of the nonlinear optical responses, we developed a nonlinear optical imaging technique that allows rapid and all-optical determination of the crystal orientations of the 2D material at a large scale. Our technique provides a route toward understanding and making use of the emerging 2D materials and devices.T he structural discontinuity at the edges and boundaries of 2D atomic materials, such as graphene and transition metal dichalcogenides, leads to complex interplay between the atomic positions and the electronic structures. Subsequently, the atomic edges and boundaries reconstruct structurally and electronically. A broad range of exceptional physical behaviors and applications including widely tunable transport gaps (1, 2), unusual magnetic responses (3-5), and high-performance nanoelectronics (6, 7) have been discovered. However, experimental observations of these 1D structures have been limited to scanning tunneling microscopy and transmission electron microscopy. Here, we studied the second-order nonlinear optics on the 1D edges and boundaries of hexagonal molybdenum disulfide (MoS 2 ) atomic membranes. The broken inversion symmetry of the atomically thin monolayer shows strong second-harmonic generation (SHG), in contrast to the centrosymmetric bulk material, which is immune to the second-order nonlinear processes. The destructive interference and annihilation of nonlinear waves from neighboring atomic membranes reveals the few-atom-wide line defects that stitch different crystal grains together, and also allows the mapping of crystal grains and grain boundaries over large areas. Our optical imaging technique enables the nonlinear optical detection of the edge states at the atomic edges of 2D crystals where the translational symmetry is broken. The observed edge resonance of SHG clearly indicates the electronic structure variation at the atomic edges, which have long been suspected to be the active sites for electrocatalytic hydrogen evolution (8).Unlike gapless graphene, the monolayer form of transition metal dichalcogenides such as MoS 2 shows a direct band gap at visible frequencies, making them emergent semiconductors for nanoelectronics and optoelectronics involving photovoltaic and/or photoemission processes (9, 10). In MoS 2 , the unique local orbital properties of the heavy transition metal atoms and broken inversion symmetry of the monolayer crystal introduce an imbalanced charge carrier distribution in momentum space, giving rise to a novel valleyspecific circular dichroism (11)(12)13). Hexagonal bulk MoS 2 ...

Recently, two-dimensional (2D) materials have opened a new paradigm for fundamental physics explorations and device applications. Unlike gapless graphene, monolayer transition metal dichalcogenide (TMDC) has new optical functionalities for next generation ultra-compact electronic and opto-electronic devices. When TMDC crystals are thinned down to monolayers, they undergo an indirect to direct bandgap transition 1, 2 , making it an outstanding 2D semiconductor [1][2][3][4][5] . Unique electron valley degree of freedom [6][7][8][9] , strong light matter interactions 10 and excitonic effects were observed [11][12][13] . Enhancement of spontaneous emission has been reported on TMDC monolayers integrated with photonic crystal 14,15 and distributed Bragg reflector microcavities 16,17 .However, the coherent light emission from 2D monolayer TMDC has not been demonstrated, mainly due to that an atomic membrane has limited material gain volume and is lack of optical mode confinement. Here, we report the first realization of 2D excitonic laser by embedding monolayer tungsten disulfide (WS 2 ) in a microdisk resonator. Using a whispering gallery mode (WGM) resonator with a high quality factor and optical confinement, we observed bright excitonic lasing in visible wavelength. The Si 3 N 4 /WS 2 /HSQ sandwich configuration provides a strong feedback and mode overlap with monolayer gain. This demonstration of 2D excitonic laser marks a major step towards 2D on-chip optoelectronics for high performance optical communication and computing applications.