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

Low-dimensional van der Waals (vdW) three-dimensional (3D) topological insulators (TIs) have been overlooked, regarding their electromechanical properties. In this study, we experimentally investigate the electromechanical coupling of low-dimensional 3D TIs with a centrosymmetric crystal structure, where a binary compound, bismuth selenide (Bi₂Se₃), is taken as an example. Piezoresponse force microscopy (PFM) results of Bi₂Se₃ nanoflakes show that the material exhibits both out-of-plane and in-plane electromechanical responses. With careful analyses, the electromechanical responses are verified to arise from the converse flexoelectricity. The Bi₂Se₃ nanoflakes have a decreasing effective out-of-plane piezoelectric coefficient d₃₃^eff with the thickness increasing, with the d₃₃^eff value of ∼0.65 pm V^-1 for the 37 nm-thick sample. The measured effective out-of-plane piezoelectric coefficient is mainly contributed by the flexoelectric coefficient, μ₃₉, which is estimated to be approximately 0.13 nC m^-1. The results can help to understand the flexoelectricity of low-dimensional vdW TIs with centrosymmetric crystal structures, which is crucial for the design of nanoelectromechanical devices and spintronics built by vdW TIs.