Electrostatic doping and hybrid carriers in graphene on a polar SrTiO$_{\mathrm{3}}$ (111) surface: theoretical investigation

Doping graphene layers presents a difficult practical and fundamental problem. We consider theoretically, the possibility of electrostatic doping of graphene by the intrinsic field of a polar substrate. By way of example, density functional theory calculations are carried out for a graphene sheet placed on the (111)-oriented perovskite SrTiO$_{\mathrm{3}}$ surface. We find that the Fermi surface moves well below the Dirac point of graphene, resulting simultaneously in a fast conducting channel in graphene, and a slow, large effective mass channel in the oxide surface. Electrostatic gating may allow one to explore peculiar states that, through the ``no-crossing'' reminiscent of polaritons, would represent a hybrid carrier that exists simultaneously in both materials. Importantly, in addition to the field doping, we identify a more ``obvious'' mechanism of doping through the contact potential difference, which may have wider applications in the doping of two-dimensional materials.