Opening and tuning of band gap by the formation of diamond superlattices in twisted bilayer graphene

We report results of first-principles density functional theory calculations, which introduce a new class of carbon nanostructures formed due to creation of covalent interlayer C-C bonds in twisted bilayer graphene (TBG). This interlayer bonding becomes possible by hydrogenation of the graphene layers according to certain hydrogenation patterns. The resulting relaxed configurations consist of two-dimensional (2D) superlattices of diamondlike nanocrystals embedded within the graphene layers, with the same periodicity as that of the Moiré pattern corresponding to the rotational layer stacking in TBG. The 2D diamond nanodomains resemble the cubic or the hexagonal diamond phase. The detailed structure of these superlattice configurations is determined by parameters that include the twist angle, ranging from 0◦ to ∼15◦, and the number of interlayer C-C bonds formed per unit cell of the superlattice. We demonstrate that formation of such interlayer-bonded finite domains causes the opening of a band gap in the electronic band structure of TBG, which depends on the density and spatial distribution of interlayer C-C bonds. We have predicted band gaps as wide as 1.2 eV and found that the band gap increases monotonically with increasing size of the embedded diamond nanodomain in the unit cell of the superlattice. Such nanostructure formation constitutes a promising approach for opening a precisely tunable band gap in bilayer graphene.