Here, we report the discovery of a new, curvature-localizing, subcritical buckling mode that produces shallow-kink corrugation in multi-layer graphene. Our density functional theory (DFT) analysis reveals the mode configuration-an approximately 2 nm wide boundary layer of highly localized curvature that connects two regions of uniformly but oppositely sheared stacks of flat atomic sheets. The kink angle between the two regions is limited to a few degrees, ensuring elastic deformation. By contrast, a purely mechanical model of sandwich structures shows progressive supercritical curvature localization spread over a 50-100 nm wide boundary layer. Our effective-locality model of electromechanics reveals that coupling between atomic-layer curvature and electric-charge polarization, i.e. quantum flexoelectricity, leads to emergence of a boundary layer in which curvature is focused primarily within a 0.86 nm fixed band width. Both DFT and the model analyses show focused distributions of curvature and polarization exhibiting oscillating decay within the approximately 2 nm wide boundary layer. The results show that dipole-dipole interaction lowers the potential energy with such a distribution. Furthermore, this model predicts peak-polarization density approximately 0.12 e- nm-1 for 3° tilt angle. This high polarization concentration can be controlled by macroscopic deformation and is expected to be useful in studies of selective graphene-surface functionalization for various applications.