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...

Manipulating a quantum state via electrostatic gating has been of great importance for many model systems in nanoelectronics. Until now, however, controlling the electron spins or, more specifically, the magnetism of a system by electric-field tuning has proven challenging. Recently, atomically thin magnetic semiconductors have attracted significant attention due to their emerging new physical phenomena. However, many issues are yet to be resolved to convincingly demonstrate gate-controllable magnetism in these two-dimensional materials. Here, we show that, via electrostatic gating, a strong field effect can be observed in devices based on few-layered ferromagnetic semiconducting CrGeTe. At different gate doping, micro-area Kerr measurements in the studied devices demonstrate bipolar tunable magnetization loops below the Curie temperature, which is tentatively attributed to the moment rebalance in the spin-polarized band structure. Our findings of electric-field-controlled magnetism in van der Waals magnets show possibilities for potential applications in new-generation magnetic memory storage, sensors and spintronics.

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.