Curvature-induced geometric potential in strain-driven nanostructures

We derive the effective dimensionally reduced Schr\"odinger equation for electrons in strain-driven curved nanostructures by adiabatic separation of fast and slow quantum degrees of freedom. The emergent strain-induced geometric potential strongly renormalizes the purely quantum curvature-induced potential and enhances the effects of curvature by several orders of magnitude. Applying this analysis to nanocorrugated thin films shows that this curvature-induced potential leads to strongly enhanced electron localization and the opening of substantial band gaps.