Ultra Long-Range Interactions in the Delamination of Atomically-Thin Layers from Substrates

Anomalous proximity effects have been experimentally observed in systems ranging from proteins, bacteria, and gecko feet suspended over semiconductor surfaces to interfaces between graphene and different substrate materials (Si, SiO2, Cu). In the latter case, long-range forces are evidenced by measurements of a non-vanishing stress that extends up to micrometer separations between graphene and the substrate. State-of-the-art models to describe adhesive properties are unable to explain these experimental observations, instead underestimating the measured distance range by 2-3 orders of magnitude. Here we develop an analytical and numerical variational approach that combines continuum mechanics and elasticity with quantum many-body treatment of van der Waals dispersion interactions between two extended objects. A full relaxation of the coupled adsorbate/substrate geometry as a function of separation leads us to conclude that wavelike atomic deformation is responsible for the observed ultra long-range stress in delamination of graphene from various substrates. Remarkably, the observed long-range proximity effect seems to be a general phenomenon for thin membranes and its correct theoretical description requires a direct coupling between quantum and continuum mechanics.