Bending of single-layer CrI₃ under spatially oscillating electric field: A first-principles study

Flexoelectricity is the interplay between the strain gradient and the electric field or polarizations, which is ubiquitous in dielectrics and much more important in two-dimensional (2D) materials due to the high flexibility. Here, we employ first-principles calculations to study the flexural deformation of the single-layer CrI₃ under a spatially oscillating electric field created by hydrogen fluoride (HF) molecular dipole arrays. It is found that the CrI₃ single-layer spontaneously wrinkles and the bending curvature exhibits a nearly quadratic dependence on the maximal electric field with a robust bending direction. This behavior is associated with the inverse flexoelectric effect, which refers to the emergence of strain gradient induced by an external electric field, but the curvature under such space-varying electric field increases faster with the electric field strength than that under a homogeneous field. Our results provides new possibility for the design of electromechanical devices in 2D materials.