The Princess and the Nanoscale Pea: Long-Range Penetration of Surface Distortions into Layered Materials Stacks

The penetration of moiré out-of-plane distortions, formed at the heterogeneous interface of graphene and hexagonal boron nitride (h-BN), into the layered h-BN stack is investigated. For aligned contacts, the estimated characteristic penetration length of ∼4.7 nm suggests that even at the far surface of a ∼25 h-BN layer thick slab stacked atop the contact, a corrugation of ∼0.1 Å, well within experimental resolution, should still be clearly evident. The penetration length is found to strongly reduce with increasing misalignment angle of the graphene/h-BN junction, where the effect of thermal fluctuations conceals the moiré-induced corrugation in the bulk. These results can be rationalized by continuum elastic theory arguments for anisotropic media. Our findings, which are expected to generally apply for layered heterojunctions, may serve as a route to control the surface corrugation, adhesive properties, and tribological characteristics of two-dimensional materials.