Precise measurement of the configurational energy of bent graphene membranes via three-dimensional force field spectroscopy

Two key parameters for mechanical properties of atomically thin membranes -- bending rigidity and Gaussian modulus -- describe the relationship between configurational (strain) energy and bending curvatures. The authors apply three-dimensional force field spectroscopy, based on atomic force microscopy (AFM), to convex-curved graphene in rolled and unrolled forms. Force-spectra analysis reveals that the configurational energy is measured precisely via the AFM tip that detects spatially varying surface potentials, owing to rehybridization effects and change in next-neighbor hopping caused by the bending curvatures.