|The small mismatch between the honeycomb lattices of graphene (GE) and boron nitrate (h-BN) leads to long wavelength Moir'e patterns. In order to describe such patterns it will require large size unit cells that are unattainable with ab-initio calculations. Earlier density functional theory calculations imposed lattice matching between graphene and h-BN which induces strain and opens a gap of 4 meV . In previous works the Moir'e pattern in GE/h-BN was connected to the van der Waals interaction , but a clear theoretical microscopic analysis is still missing. We used atomistic simulations  with very large unit cells to investigate quantitative aspects of the connection between the vdW interaction and the Moir'e patterns. The value and symmetry of the spatial dependent vdW energy is obtained which agrees with the recently reported Moir'e patterns.
Dr. Mehdi Neek-Amal
20 Nov. 2014