Sub-nm Curvature Unlocks Quantum Flexoelectricity in Graphene

Flexoelectricity, polarization induced by strain gradients, is especially pronounced in two-dimensional (2D) materials due to their mechanical flexibility and sensitivity to mechanical deformation. In nanostructures with sub-nm curvature, this effect is governed by quantum-mechanical polarization and electrostatic modulation, not merely classical lattice distortion. Here, we present the first direct experimental and theoretical demonstration of large intrinsic quantum flexoelectricity in graphene nanowrinkles, exhibiting polarization densities (P_{th} ~ 4 C/m^{2}, P_{exp} ~ 1 C/m^{2}) that exceed those of mesoscale systems by 5 to 7 orders of magnitude. These nanowrinkles, with sub-nm radii of curvature at their apex, undergo atomic-level buckling and result in localized strain fields, as confirmed by sub-micron Raman spectroscopy. These curvatures create an asymmetry to {\pi}-orbital interactions across the atomic layer, which, in turn, leads to localized polarization densities. Kelvin probe force microscopy reveals curvature-dependent work function shifts consistent with flexoelectric polarization, while conductive atomic force microscopy detects reproducible flexoelectric currents exhibiting a threshold voltage ({\Phi}th ~1 V) that matches the band offset predicted by ab initio calculations (~1.2 V). Together, these results confirm how flexoelectric dipoles reshape the local electronic potential. Graphene nanowrinkles thus provide a pristine platform for uncovering quantum-mechanical flexoelectricity: a fundamentally ubiquitous effect, whose study in the simplest crystalline material can illuminate electromechanical behavior across condensed matter, soft matter, and biological systems.