Prediction of Nonlinear Flexoelectricity in Monolayer CrI₃

Flexoelectricity, the modification of electric polarization induced by strain gradients, is ubiquitous in all materials and is typically a minor effect in bulk materials represented as a linear function of curvature. However, in 2D materials, the curvature can be dramatically large due to their flexibility, which naturally raises an intriguing question of whether flexoelectricity extends beyond the linear form. Here, we reveal a type of nonlinear flexoelectricity that depends on both the curvature and its gradients through first-principles calculations. This nonlinear flexoelectric effect only presents in certain materials such as monolayer CrI₃, which is a consequence of the simultaneous breaking of the in-plane and out-of-plane mirror symmetries perpendicular to the curvature direction. In contrast, materials like graphene, h-BN, and 2H-WTe₂ monolayers with no such symmetry breaking do not present such a nonlinear flexoelectric effect. Furthermore, a method to detect the nonlinear felexoelectricity is also proposed. Our research thus enriches the spectrum of flexophysics and has potential applications in flexoelectrics.