Geometric and electronic structure of multilayered graphene: synergy of the nondirective ripples and the number of layers

According to the Mermin–Wagner theorem, ripple deformation is ubiquitous in a two-dimensional (2D) free-standing sheet, influencing the electronic properties. However, the synergistic effects of the unrestricted ripples and the number of layers have still been a topic of extensive debate. To address this issue, we employed density functional theory including many-body van der Waals (vdW) correction to investigate the effects of the nondirective ripples on the geometric and electronic structures of multilayered graphene. We found that the many-body effects of vdW forces were essential for the binding of multilayered rippled graphene. The increase of curvature affects the electronic structures of rippled graphene by modifying stacking modes, while the increase in the number of layers can reduce band gap and work function directly. The coupling of these two effects can enhance the chemical activity of rippled graphene. Our results facilitate new insights into the geometric and electronic properties of rippled graphene, which can be generalized to other layered materials.