▎ 摘　　要

Graphene holds great promise for post-silicon electronics; however, it faces two main challenges: opening up a band gap and finding a suitable substrate material. In principle, graphene on hexagonal boron nitride (hBN) substrate provides a potential system to overcome these challenges. Recent theoretical and experimental studies have provided conflicting results: while theoretical studies suggested a possibility of a finite hand gap of graphene on hBN, recent experimental studies find no band gap. Using the first-principles density functional method and the many-body perturbation theory, we have studied graphene on hBN substrate. A Bernal stacked graphene on hBN has a band gap on the order of 0.1 eV, which disappears when graphene is misaligned with respect to hBN. The latter is the likely scenario in realistic devices. In contrast, if graphene supported on hBN is hydrogenated, the resulting system (graphone) exhibits band gaps larger than 2.5 eV. While the band gap opening in graphene/hBN is due to symmetry breaking and is vulnerable to slight perturbation such as misalignment, the graphone band gap is due to chemical functionalization and is robust in the presence of misalignment. The band gap of graphone reduces by about 1 eV when it is supported on hBN due to the polarization effects at the graphone/hBN interface. The band offsets at graphone/hBN interface indicate that hBN can be used not only as a substrate but also as a dielectric in the field effect devices employing graphone as a channel material. Our study could open up new way of band gap engineering in graphene based nanostructures.