title: Observation of piezoelectricity in free-standing monolayer MoS₂.
abstract: Piezoelectricity allows precise and robust conversion between electricity and mechanical force, and arises from the broken inversion symmetry in the atomic structure. Reducing the dimensionality of bulk materials has been suggested to enhance piezoelectricity. However, when the thickness of a material approaches a single molecular layer, the large surface energy can cause piezoelectric structures to be thermodynamically unstable. Transition-metal dichalcogenides can retain their atomic structures down to the single-layer limit without lattice reconstruction, even under ambient conditions. Recent calculations have predicted the existence of piezoelectricity in these two-dimensional crystals due to their broken inversion symmetry. Here, we report experimental evidence of piezoelectricity in a free-standing single layer of molybdenum disulphide (MoS₂) and a measured piezoelectric coefficient of e₁₁ = 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 MoS₂ 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.
authors.affiliation: NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA.
authors.forename: Hanyu
authors.initials: H
authors.lastname: Zhu
authors.affiliation: NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Wang
authors.affiliation: NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA.
authors.forename: Jun
authors.initials: J
authors.lastname: Xiao
authors.affiliation: NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA.
authors.forename: Ming
authors.initials: M
authors.lastname: Liu
authors.affiliation: NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA.
authors.forename: Shaomin
authors.initials: S
authors.lastname: Xiong
authors.affiliation: NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA.
authors.forename: Zi Jing
authors.initials: ZJ
authors.lastname: Wong
authors.affiliation: NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA.
authors.forename: Ziliang
authors.initials: Z
authors.lastname: Ye
authors.affiliation: NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA.
authors.forename: Yu
authors.initials: Y
authors.lastname: Ye
authors.affiliation: 1] NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA [2] Material Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
authors.forename: Xiaobo
authors.initials: X
authors.lastname: Yin
authors.affiliation: 1] NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA [2] Material Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
authors.forename: Xiang
authors.initials: X
authors.lastname: Zhang
mesh_terms: D003460:Crystallization; D004220:Disulfides / Q000737:chemistry*; D008982:Molybdenum / Q000737:chemistry*
chemical_list: D004220:Disulfides; D008982:Molybdenum; C082964:molybdenum disulfide