Converse Flexoelectricity in van der Waals (vdW) Three-Dimensional\nTopological Insulator Nanoflakes

Low-dimensional van\nder Waals (vdW) three-dimensional (3D) topological\ninsulators (TIs) have been overlooked, regarding their electromechanical\nproperties. In this study, we experimentally investigate the electromechanical\ncoupling of low-dimensional 3D TIs with a centrosymmetric crystal\nstructure, where a binary compound, bismuth selenide (Bi<sub>2</sub>Se<sub>3</sub>), is taken as an example. Piezoresponse force microscopy\n(PFM) results of Bi<sub>2</sub>Se<sub>3</sub> nanoflakes show that\nthe material exhibits both out-of-plane and in-plane electromechanical\nresponses. With careful analyses, the electromechanical responses\nare verified to arise from the converse flexoelectricity. The Bi<sub>2</sub>Se<sub>3</sub> nanoflakes have a decreasing effective out-of-plane\npiezoelectric coefficient <i>d</i><sub>33</sub><sup>eff</sup> with the thickness increasing, with\nthe <i>d</i><sub>33</sub><sup>eff</sup> value of ∼0.65 pm V<sup>–1</sup> for the\n37 nm-thick sample. The measured effective out-of-plane piezoelectric\ncoefficient is mainly contributed by the flexoelectric coefficient,\nμ<sub>39</sub>, which is estimated to be approximately 0.13\nnC m<sup>–1</sup>. The results can help to understand the flexoelectricity\nof low-dimensional vdW TIs with centrosymmetric crystal structures,\nwhich is crucial for the design of nanoelectromechanical devices and\nspintronics built by vdW TIs.