Sub-Nanometer Curvature Unlocks Quantum Orbital Flexoelectricity in Graphene.

Abstract

Flexoelectricity, defined as polarization induced by strain gradients, is especially pronounced in two-dimensional (2D) materials due to their mechanical flexibility and sensitivity to deformation. In nanostructures with nanometer-scale curvature, bending can perturb out-of-plane π orbitals and generate quantum-mechanical polarization and electrostatic modulation beyond classical lattice distortion alone. Here, we combine scanning probe measurements and first-principles calculations to provide experimental and theoretical evidence for large intrinsic quantum orbital flexoelectricity in graphene nanowrinkles (GNWrs) with estimated polarization densities of P_th ∼ 4 C m^-2 and P_exp ∼ 1 C m^-2, exceeding those of mesoscale systems by 5 to 7 orders of magnitude. These GNWrs exhibit high apex curvature, undergo atomic-level buckling, and produce localized strain fields, as supported by atomic force microscopy analysis and Raman spectroscopy. Kelvin probe force microscopy reveals curvature-dependent work-function shifts, while conductive atomic force microscopy detects reproducible GNWr-associated currents with a threshold voltage (Φ_th ∼ 1 V) comparable to the band offset predicted by ab initio calculations (∼ 1.2 V). These results support an interpretation in which curvature-induced flexoelectric dipoles reshape the local electronic potential. GNWrs therefore provide a structurally simple carbon-based platform for probing quantum-mechanical flexoelectricity.