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Moir'e patterns in the pseudo-magnetic field and in the strain profile ofgraphene (GE) when put on top of a hexagonal lattice substrate are predictedfrom elasticity theory. %which are confirmed by atomistic simulations. The vander Waals (vdW) interaction between GE and the substrate induces out-of-planedeformations in graphene which results in a strain field, and consequently in apseudo-magnetic field. When the misorientation angle is about 0.5 deg. athree-fold symmetric strain field is realized that results in a pseudo-magneticfield very similar to the one proposed by F. Guinea, M. I. Katsnelson, and A.K. Geim [Nat. Phys. 6, 30 (2010)]. Our results show that the periodicity andlength of the pseudo-magnetic field can be tuned in GE by changing themisorientation angle and substrate adhesion parameters and a considerableenergy gap (23 meV) can be obtained due to out-of-plane deformation of graphenewhich is in the range of recent experimental measurements (20-30 meV).

Graphene on hexagonal lattice substrate: Stress and Pseudo-magnetic field