Snap-through instability of graphene on substrates

We determine the graphene morphology regulated by substrates with herringbone and checkerboard surface corrugations. As the graphene/substrate interfacial bonding energy and the substrate surface roughness vary, the graphene morphology snaps between two distinct states: 1) closely conforming to the substrate and 2) remaining nearly flat on the substrate. Such a snapthrough instability of graphene can potentially lead to desirable electronic properties to enable graphene-based devices.