Graphene-hexagonal boron nitride van der Waals heterostructures: an examination of the effects of different van der Waals corrections

The structural and electronic properties of graphene on hexagonal boron nitride (hBN) as 2D van der Waals heterostructure were calculated using density functional theory method with van der Waals corrections. Four van der Waals corrections, along with conventional PBE-DFT, were utilized: the inter-atomic potentials-based DFT-D2, DFT-D3, Tkatchenko-Sheffler (TS), and the ab-initio, non-local correlation terms-based vdW-DF2-B86R. Results show that the structural properties of the 2D heterostructure, especially the inter-monolayer spacing, are consistent with previous theoretical works. In terms of energetics, the conventional PBE-DFT functional resulted to no binding between graphene and hBN, while utilizing the TS correction resulted to graphene-hBN adhesion energy value that is consistent with previous theoretical and experimental works. Electronic structure wise, the conventional PBE-DFT essentially predicted a zero-gap graphene on hBN, while all calculations involving van der Waals corrections resulted to band gaps that are consistent with previous studies. However, with the exception of TS, all van der Waals corrections predicted a Dirac cone that is shifted upward in energy from the Fermi level, making graphene artificially p-doped. As such, TS is recommended as one of the most appropriate van der Waals corrections for graphene-hBN 2D heterostructure. This work demonstrated the variations in graphene-hBN electronic properties as a result of the different implementations of the van der Waals corrections, but could be as useful as the more expensive theoretical methods such as GW.