Micrometer-Scale Stress from van der Waals Interactions in the Delamination of Graphene from Substrates

Anomalous long-range non-bonded interactions have been experimentally observed in many different systems, e.g. interfaces between graphene and different substrate materials (Si, SiO$_2$, Cu foils). In this case, long-range forces are evidenced by measurements of non-vanishing stress that extends up to micrometer separations between graphene and the substrate. Existing classical approaches to describe adhesive properties are unable to explain these experimental observations, instead underestimating the measured distance range by a factor of 100 to 1000. Here we develop an analytical and numerical variational approach based on pairwise and/or many-body treatment of van der Waals dispersion interactions between two extended objects. A full relaxation of the coupled adsorbate/substrate geometry leads us to conclude that the wavelike deformation of carbon atoms in graphene (and possibly the substrate) is responsible for the observed ultra long-range stress in delamination of graphene from various substrates. Remarkably, the observed emergent stress seems to be a general phenomenon for stable deformable membranes and its correct description requires a quantum-mechanical many body treatment of interatomic interactions beyond the standard pairwise models for the van der Waals energy.