Density functional theory based study of graphene and dielectric oxide interfaces.

We study the effects of insulating oxides in their crystalline forms on the energy band structure of monolayer and bilayer graphene using a first principles density functional theory based electronic structure method and a local density approximation. We consider the dielectric oxides SiO(2) (α-quartz) and Al(2)O(3) (alumina or α-sapphire), each with two surface terminations. Our study suggests that atomic relaxations and resulting equilibrium separations play a critical role in perturbing the linear band structure of graphene in contrast to the less critical role played by dangling bonds that result from cleaving the crystal in a particular direction. For Si-terminated quartz a Dirac cone is retained while it is restored on adding a second graphene layer for O-terminated quartz. Alumina needs more than two graphene layers to preserve the Dirac cone. Our results are, at best, semi-quantitative for the common amorphous forms of the oxides considered.