Probing Effective Out-of-Plane Piezoelectricity in van der Waals Layered Materials Induced by Flexoelectricity.

Many van der Waals layered 2D materials, such as h-BN, transition metal dichalcogenides (TMDs), and group-III monochalcogenides, have been predicted to possess piezoelectric and mechanically flexible natures, which greatly motivates potential applications in piezotronic devices and nanogenerators. However, only intrinsic in-plane piezoelectricity exists in these 2D materials and the piezoelectric effect is confined in odd-layers of TMDs. The present work is intent on combining the free-standing design and piezoresponse force microscopy techniques to obtain and directly quantify the effective out-of-plane electromechanical coupling induced by strain gradient on atomically thin MoS2 and InSe flakes. Conspicuous piezoresponse and the measured piezoelectric coefficient with respect to the number of layers or thickness are systematically illustrated for both MoS2 and InSe flakes. Note that the promising effective piezoelectric coefficient (deff 33 ) of about 21.9 pm V-1 is observed on few-layered InSe. The out-of-plane piezoresponse arises from the net dipole moment along the normal direction of the curvature membrane induced by strain gradient. This work not only provides a feasible and flexible method to acquire and quantify the out-of-plane electromechanical coupling on van der Waals layered materials, but also paves the way to understand and tune the flexoelectric effect of 2D systems.