Potential energy surface for graphene on graphene:Ab initioderivation, analytical description, and microscopic interpretation

We derive an analytical expression that describes the interaction energy between two graphene layers identically oriented as a function of the relative lateral and vertical positions, in excellent agreement with first principles calculations. Thanks to its formal simplicity, the proposed model allows for an immediate interpretation of the interactions, in particular of the potential corrugation. This last quantity plays a crucial role in determining the intrinsic resistance to interlayer sliding and its increase upon compression influences the frictional behavior under load. We show that, for these weakly adherent layers, the corrugation possesses the same nature and $z$ dependence of Pauli repulsion. We investigate the microscopic origin of these phenomena by analyzing the electronic charge distribution: We observe a pressure-induced charge transfer from the interlayer region toward the near-layer regions, with a much more consistent depletion of charge occurring for the $AA$ stacking than for the $AB$ stacking of the two layers.