Smoothing effects of two-dimensional materials

Rippling in graphene, which is an out-of-plane corrugation induced by thermal fluctuations, plays a fundamental role in supporting the material’s stable existence. These ripples have also been instrumental in explaining various unconventional electronic and chemical properties of graphene. Previous experimental findings have indicated that graphene exhibits smoothing effects on underlying substrates in the high-spatial-frequency regime. To explain this phenomenon, we employed a force balance model that considered both van der Waals forces and strain forces. By utilizing traditional film-growth theory, our model successfully predicted experimental results.