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

Abstract

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 d ₃₃ ^eff with the thickness increasing, with the d ₃₃ ^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.

Figure 1

Sample characterization. (a) Optical microscopy image of the as-prepared Bi₂Se₃ flakes on a gold-coated Si/SiO₂ substrate. (b) Contact-mode AFM topography image and (c) the corresponding height profile along the dashed line in (b) of the Bi₂Se₃ nanoflake in the framed region in (a). (d) Schematic of the crystal structure of Bi₂Se₃.

Figure 2

VPFM measurements of an individual Bi₂Se₃ nanoflake with a thickness of 37 nm. Contact-mode AFM images of the nanoflake under AC voltages of (a) 0 and (b) 7 V, respectively. VPFM amplitude images measured at AC voltages of (c) 0, (d) 3, (e) 5, and (f) 7 V, respectively. Scale bars: 2 μm.

Figure 3

Geometry of the conductive AFM tip and contact of the tip with flat Bi₂Se₃. (a) SEM image of the used AFM conductive tip. ρ represents the radius of the tip head, which is 10 nm. (b) Zoomed-in SEM image of the framed area in panel a. (c, d) Models of distribution of the out-of-plane (along the z direction) electric field E_z (denoted as E₃) and gradient (, denoted as E_3,3) of E_z inside the Bi₂Se₃ plate below the tip apex, respectively, under an voltage of 8 V. The tip shape is set to be consistent with the one shown in (b). The thickness of the Bi₂Se₃ plate is 10 nm. (e, f) Line curves of E₃ and E_3,3 along the z direction.

Figure 4

Out-of-plane electromechanical properties of Bi₂Se₃ nanoflakes. VPFM amplitude as a function of the applied AC voltage for (a) the nanoflake with a thickness of 37 nm and (b) nanoflakes with different thicknesses. (c) AFM topography image of a Bi₂Se₃ nanoflake with a thickness of 49 nm and (d) the corresponding KPFM image. (e) AFM topography image of a Bi₂Se₃ nanoflake with a thickness of 109 nm and (f) the corresponding KPFM image. Scale bars, 5 μm. (g) Statistical distribution of the surface potential of the framed regions in (d) and (f), corresponding to Au, the thin Bi₂Se₃ nanoflake and the thick Bi₂Se₃ nanoflake, respectively.

Figure 5

LPFM measurements of an individual Bi₂Se₃ nanoflake with a thickness of ∼40 nm. (a) AFM topography of the Bi₂Se₃ nanoflake. (b) LPFM amplitude as a function of the applied AC voltage. (c–h) In-plane PFM amplitude images of the framed region in (a) with applied AC voltages of 0, 1, 3, 5, 7, and 9 V, respectively. Scale bars: 1 μm.