Ab initio study of the relationship between spontaneous polarization and   p-type doping in quasi-freestanding graphene on H-passivated SiC surfaces
  Quasi-free standing graphene (QFG) obtained by the intercalation of a hydrogen layer between a SiC surface and the graphene is recognized as an excellent candidate for the development of graphene based technology. In addition, the recent proposal of a direct equivalence between the $p$-type doping typically found for these systems and the spontaneous polarization (SP) associated to the particular SiC polytype, opens the possibility of tuning the number of carriers in the Dirac cones without the need of external gate voltages. However, first principles calculations which could confirm at the atomic scale the effect of the SP are lacking mainly due to the difficulty of combining a bulk property such as the SP with the surface confined graphene doping. Here we develop an approach based on standard density functional theory (DFT) slab calculations in order to quantify the effect of the SP on the QFG doping level. First, we present an accurate scheme to estimate the SPs by exploiting the dependence of the slab's dipole moment with its thickness. Next, and in order to circumvent the DFT shortcomings associated to polar slab geometries, a double gold layer is attached at the C-terminated bottom of the slab which introduces a metal induced gap state that pins the chemical potential inside the gap thus allowing a meaningful comparison of the QFG dopings among different polytypes. Furthermore, the slab dipole can be removed after adjusting the Au-Au interlayer distances. Our results confirm that the SP does indeed induce a substantial p-doping of the Dirac cones which can be as large as a few hundreds of meV depending on the hexagonality of the polytype. The evolution of the doping with the slab thickness reveals that several tens of SiC bilayers are required to effectively remove the depolarization field and recover the macroscopic regime whereby the graphene doping should equal the SP. 
J. Slawinska, H. Aramberri, M.C. Mu\~noz, J. I. Cerd\'a
cond-mat.mtrl-sci