Edge Nonlinear Optics on a MoS2 Atomic Monolayer
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
... sing 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 nano-electronics 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 has a layered structure with a single layer of molybdenum atoms sandwiched between two layers of sulfur atoms in a trigonal prismatic lattice. Each unit cell is formed by two mirrored sublattices, making the bulk crystal centrosymmetric and prohibiting the second-order nonlinear optical processes therein. However, in a monolayer consisting of one layer of molybdenum atoms and two sulfur atom layers, or few-layer MoS 2 with oddnumbered layers, the inversion center is removed, resulting in a strong second-order nonlinear optical response. The origins of the strong nonlinear optical responses and their symmetry properties have been discussed (14-16). The observed oscillatory nonlinearity between the odd-numbered and evennumbered layers is unique to all layered transition metal dichalcogenides, including MoS 2 and WSe 2 (17). Because SHG is strongly affected by the lowered symmetry of a material, the structure and symmetry properties of MoS 2 atomic membranes can be probed by second-harmonic emission, which allows us to demonstrate the nonlinear optical properties of these 2D materials. Figure 1 shows the linear and nonlinear optical images of a continuous monolayer MoS 2 membrane epitaxially grown by chemical vapor deposition (CVD) (18). Oxide-onsilicon substrates with oxide films 285 nm thick were used for optimized optical contrast. The monolayer samples show high-quality photoluminescence and are optically uniform over large areas (Fig. 1A) . In contrast, the SHG image (Fig. 1B) reveals the polycrystalline nature of the uniform monolayer, and the average grain size ranges from 20 to 40 mm. Here, the incident polarization of the pump beam is along the y axis and the total second-harmonic radiation is collected. The uniform SHG intensity within each grain indicates that the individual grains REPORTS Fig. 1. All-optical determination of the crystal orientations of MoS 2 atomic membranes. (A) Optical image of a large area of CVD-grown monolayer MoS 2 . (B) SHG image of a polycrystalline monolayer of MoS 2 of the same area. The grains and grain boundaries are clearly revealed by the reduced SHG intensity at the boundaries. The crystals are connected by faceted, abrupt grain boundaries. The scattered bright spots are from the nanocrystals produced in the vapor growth process. The average monolayer crystal sizes are between 20 and 50 mm. (C) The direct crystal orientation image shows the crystal orientations of the irregular-shaped polycrystalline aggregates. (D) Schematics show the flakes I and II are two crystals with opposite orientations, as they have the same contrast in crystal orientation maps but a strongly destructive interference boundary. Crystals II and III show an orientation mismatch of~12°. The crystal groups a and b show two cyclic twin boundaries with 60°(a) and 30°(b), respectively. Scale bar, 40 mm.