Stacking in incommensurate graphene/hexagonal-boron-nitride heterostructures based on ab initio study of interlayer interaction

摘要

The interlayer interaction in graphene/boron-nitride heterostructures isstudied using density functional theory calculations with the correction forvan der Waals interactions. It is shown that the use of the experimentalinterlayer distance allows to describe the potential energy surface at thelevel of more accurate but expensive computational methods. On the other hand,it is also demonstrated that the dependence of the interlayer interactionenergy on the relative in-plane position of the layers can be fitted with highaccuracy by a simple expression determined by the system symmetry. The use ofonly two independent parameters in such an approximation suggests that variousphysical properties of flat graphene/boron-nitride systems are interrelated andcan be expressed through these two parameters. Here we estimate some of thecorresponding physical properties that can be accessed experimentally,including the correction to the period of the Moir\'{e} superstructure for thehighly incommensurate ground state of graphene/boron-nitride bilayer comingfrom the interlayer interaction, width of stacking dislocations in slightlyincommensurate systems of boron nitride on stretched graphene and shear modefrequencies for commensurate graphene/boron-nitride systems, such as a flake ona layer. We propose that the commensurate-incommensurate phase transition canbe observed in boron nitride on stretched graphene and experimentalmeasurements of the corresponding critical strain can be also used to get aninsight into graphene/boron-nitride interactions.