Unusual Flexoelectric Effect in Two-Dimensional Noncentrosymmetric sp2-Bonded Crystals

We find, with the use of the first-principles calculations, that the single-atom-thick sp(2)-bonded noncentrosymmetric crystals like boron-nitride (BN) sheet exhibit an unusual nonlinear electromechanical effect: they become strongly macroscopically polarized in a corrugated state (or it induces significant changes in an initially polarized state of a sheet like BC2N). The direction of the induced polarization is in a plane of the film and depends nonanalytically on the corrugation wave vector k. The magnitude of the polarization can reach very large values in spite of its quadratic dependence on atomic displacements due to BN sheets being able to tolerate very large mechanical strains, similar to carbon nanotubes, and this makes this general behavior of noncentrosymmetric bodies perturbed out of equilibrium quite unique. The effect may find various applications, in particular, in a new type of nanogenerators.