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The spin Hall effect (SHE) of light is very weak because of the extremely small photon momentum and spin-orbit interaction. Here, we report a strong photonic SHE resulting in a measured large splitting of polarized light at metasurfaces. The rapidly varying phase discontinuities along a metasurface, breaking the axial symmetry of the system, enable the direct observation of large transverse motion of circularly polarized light, even at normal incidence. The strong spin-orbit interaction deviates the polarized light from the trajectory prescribed by the ordinary Fermat principle. Such a strong and broadband photonic SHE may provide a route for exploiting the spin and orbit angular momentum of light for information processing and communication.

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 ...

Piezoelectricity allows precise and robust conversion between electricity and mechanical force, and arises from the broken inversion symmetry in the atomic structure [1][2][3] . Reducing the dimensionality of bulk materials has been suggested to enhance piezoelectricity 4 . However, when the thickness of a material approaches a single molecular layer, the large surface energy can cause piezoelectric structures to be thermodynamically unstable 5 . Transition-metal dichalcogenides can retain their atomic structures down to the single-layer limit without lattice reconstruction, even under ambient conditions 6 . Recent calculations have predicted the existence of piezoelectricity in these two-dimensional crystals due to their broken inversion symmetry 7 . Here, we report experimental evidence of piezoelectricity in a free-standing single layer of molybdenum disulphide (MoS 2 ) and a measured piezoelectric coefficient of e 11 = 2.9 × 10 -10 C m −1 . The measurement of the intrinsic piezoelectricity in such free-standing crystals is free from substrate effects such as doping and parasitic charges. We observed a finite and zero piezoelectric response in MoS 2 in odd and even number of layers, respectively, in sharp contrast to bulk piezoelectric materials. This oscillation is due to the breaking and recovery of the inversion symmetry of the two-dimensional crystal. Through the angular dependence of electromechanical coupling, we determined the two-dimensional crystal orientation. The piezoelectricity discovered in this single molecular membrane promises new applications in low-power logic switches for computing and ultrasensitive biological sensors scaled down to a single atomic unit cell 8,9 .Since its discovery in 1880, piezoelectricity has found a wide range of applications in actuation, sensing and energy harvesting. The rapidly growing demand for high-performance and miniaturized devices in micro-electro-mechanical systems (MEMS) and electronics 10-12 calls for nanoscale piezoelectric materials, motivating theoretical investigations into novel low-dimensional systems such as nanotubes and single molecules 13,14 . Transition-metal dichalcogenides (TMDCs) are ideal candidates as low-dimensional piezoelectric materials because of their structural non-centrosymmetry 7 . Although there has been extensive research interest in the unique properties originating from such symmetry breaking, including circular dichroism and second harmonic generation (SHG) [15][16][17][18][19] , experimental quantitative determination of the intrinsic piezoelectric properties of these two-dimensional crystals has yet to be demonstrated. Here, we report the observation of piezoelectricity in freestanding monolayer MoS 2 membranes. Interestingly, we found that this molecular piezoelectricity only exists when there are an odd number of layers in the two-dimensional crystal where inversion symmetry breaking occurs. We observed an angular dependence of the piezoelectric response in agreement with the three-fold symmetry of the crystal, and based...

Hyperlenses have generated much interest recently, not only because of their intriguing physics but also for their ability to achieve sub-diffraction imaging in the far field in real time. All previous efforts have been limited to sub-wavelength confinement in one dimension only and at ultraviolet frequencies, hindering the use of hyperlenses in practical applications. Here, we report the first experimental demonstration of far-field imaging at a visible wavelength, with resolution beyond the diffraction limit in two lateral dimensions. The spherical hyperlens is designed with flat hyperbolic dispersion that supports wave propagation with very large spatial frequency and yet same phase speed. This allows us to resolve features down to 160 nm, much smaller than the diffraction limit at visible wavelengths, that is, 410 nm. The hyperlens can be integrated into conventional microscopes, expanding their capabilities beyond the diffraction limit and opening a new realm in real-time nanoscopic optical imaging.

We report efficient nonradiative energy transfer (NRET) from core-shell, semiconducting quantum dots to adjacent two-dimensional sheets of graphene and MoS2 of single- and few-layer thickness. We observe quenching of the photoluminescence (PL) from individual quantum dots and enhanced PL decay rates in time-resolved PL, corresponding to energy transfer rates of 1-10 ns(-1). Our measurements reveal contrasting trends in the NRET rate from the quantum dot to the van der Waals material as a function of thickness. The rate increases significantly with increasing layer thickness of graphene, but decreases with increasing thickness of MoS2 layers. A classical electromagnetic theory accounts for both the trends and absolute rates observed for the NRET. The countervailing trends arise from the competition between screening and absorption of the electric field of the quantum dot dipole inside the acceptor layers. We extend our analysis to predict the type of NRET behavior for the near-field coupling of a chromophore to a range of semiconducting and metallic thin film materials.

Second-harmonic generation (SHG) has found extensive applications from hand-held laser pointers to spectroscopic and microscopic techniques. Recently, some cleavable van der Waals (vdW) crystals have shown SHG arising from a single atomic layer, where the SH light elucidated important information such as the grain boundaries and electronic structure in these ultra-thin materials. However, despite the inversion asymmetry of the single layer, the typical crystal stacking restores inversion symmetry for even numbers of layers leading to an oscillatory SH response, drastically reducing the applicability of vdW crystals such as molybdenum disulfide (MoS2). Here, we probe the SHG generated from the noncentrosymmetric 3R crystal phase of MoS2. We experimentally observed quadratic dependence of second-harmonic intensity on layer number as a result of atomically phase-matched nonlinear dipoles in layers of the 3R crystal that constructively interfere. By studying the layer evolution of the A and B excitonic transitions in 3R-MoS2 using SHG spectroscopy, we also found distinct electronic structure differences arising from the crystal structure and the dramatic effect of symmetry and layer stacking on the nonlinear properties of these atomic crystals. The constructive nature of the SHG in this 2D crystal provides a platform to reliably develop atomically flat and controllably thin nonlinear media.

Electrically controlling the flow of charge carriers is the foundation of modern electronics. By accessing the extra spin degree of freedom (DOF) in electronics, spintronics allows for information processes such as magnetoresistive random-access memory. Recently, atomic membranes of transition metal dichalcogenides (TMDCs) were found to support unequal and distinguishable carrier distribution in different crystal momentum valleys. This valley polarization of carriers enables a new DOF for information processing. A variety of valleytronic devices such as valley filters and valves have been proposed, and optical valley excitation has been observed. However, to realize its potential in electronics it is necessary to electrically control the valley DOF, which has so far remained a significant challenge. Here, we experimentally demonstrate the electrical generation and control of valley polarization. This is achieved through spin injection via a diluted ferromagnetic semiconductor and measured through the helicity of the electroluminescence due to the spin-valley locking in TMDC monolayers. We also report a new scheme of electronic devices that combine both the spin and valley DOFs. Such direct electrical generation and control of valley carriers opens up new dimensions in utilizing both the spin and valley DOFs for next-generation electronics and computing.