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The mechanical and electronic properties of a graphene membrane placed on topof a superlattice of nanopillars are investigated. We use molecular dynamics(MD) simulations to access the deformation fields and the tight-bindingapproaches to calculate the electronic properties. The system of interestconsists of a triangular lattice of nanopillars with a period of a=750 nm overwhich the graphene layer is deposited. Ripples form in the graphene layer thatspan across the unit cell, connecting neighbouring pillars, in agreement withrecent experiments. We find that the resulting pseudo-magnetic field (PMF)varies strongly across the unit cell. We investigate the dependence of PMF onunit cell boundary conditions, height of the pillars, and the strength of thevan der Waals interaction between graphene and the substrate. We find directcorrespondence with typical experiments on pillars, showing intrinsic "slack"in the graphene membrane. PMF values are confirmed by the local density ofstates calculations performed at different positions of the unit cell showingpseudo-Landau levels at varying spacings. Our findings regarding the relaxedmembrane configuration and the induced strains are transferable to otherflexible 2D membranes.

Strain field in graphene induced by nanopillar mesh