By atomistic modeling of moiré patterns of graphene on a substrate with a small lattice mismatch, we find qualitatively different strain distributions for small and large misorientation angles, corresponding to the commensurate-incommensurate transition recently observed in graphene on hexagonal BN. We find that the ratio of C-N and C-B interactions is the main parameter determining the different bond lengths in the center and edges of the moiré pattern. Agreement with experimental data is obtained only by assuming that the C-B interactions are at least twice weaker than the C-N interactions. The correspondence between the strain distribution in the nanoscale moiré pattern and the potential energy surface at the atomic scale found in our calculations, makes the moiré pattern a tool to study details of dispersive forces in van der Waals heterostructures. The study of these new hybrid materials is emerging as a strong research area.The superposition of periodic layered structures, with either slightly different lattice constants or different orientations, creates moiré patterns [3][4][5][6][7]. These patterns can yield a wealth of information about the lattice constant mismatch, strain and imperfections of the surface [8][9][10][11][12][13]. The moiré patterns imply a change of the interatomic distances that can affect properties that are important both for applications and for fundamental physics such as the quantum mechanics of electrons in quasi-periodic potentials [3][4][5][6].In recent years hexagonal boron nitride (h-BN) has become a standard substrate for graphene growth due to its flat surface without dangling bonds, the hexagonal lattice with a lattice constant only 1.8 % larger than that of graphene and the fact that h-BN is an insulator [14]. These properties have led to the realization of the first field effect transistor [15]. The difference in lattice constant leads to the appearances of moiré patterns, which can be observed experimentally [16][17][18].Usually, moiré structures are considered from a purely geometrical point of view for the superposition of two rigid lattices where the length L of the moiré patterns is found to depend on the angle θ and the lattice mismatch between the two layers aswhere p is the ratio between lattice constants and a the lattice constant of the substrate [19]. Strain due to the lattice mismatch and/or rotations have been considered in a continuum approach to study the modification of the electronic structures in tight binding calculations [20][21][22][23][24] and the pseudo-magnetic fields resulting from out-of-plane displacements [25,26]. Full atomic relaxation to minimal energy configurations is however necessary to make a detailed comparison to experimental structural information as obtained by scanning probe microscopy [7]. At the same time, we will show that this procedure allows to get quantitative information on the interplanar interactions. It is well known that dispersive forces are beyond the standard local density functional and generalized gradient correct...

Abstract. We study the effect of atomic relaxation on the structure of moiré patterns in twisted graphene on graphite and double layer graphene by large scale atomistic simulations. The reconstructed structure can be described as a superlattice of 'hot spots' with vortex-like behaviour of in-plane atomic displacements and increasing out-of-plane displacements with decreasing angle. These lattice distortions affect both scalar and vector potential and the resulting electronic properties. At low misorientation angles (<∼1• ) the optimized structures deviate drastically from the sinusoidal modulation which is often assumed in calculations of the electronic properties. The proposed structure might be verified by scanning probe microscopy measurements.arXiv:1503.02540v1 [cond-mat.mes-hall]