Few-layer and symmetry-breaking effects on the electrical properties of ordered CF$_3$Cl phases on graphene*

An effective pseudopotential mechanism for breaking the inherent sub-lattice symmetry of graphene has been studied using DFT calculations on hexagonal boron nitride.\footnote{Gianluca Giovannetti et al.\ , PRB 76, 073103 (2007)} Electrical detection of CF$_3$Cl phase transitions on graphene shows the existence of a commensurate ordered phase in which this can be tested.\footnote{Yilin Wang et al.\ , APL 103, 201606 (2013)} We study the electronic properties of this phase using VASP ver 5.3.3, with ab initio van der Waals density functionals (vdW-DF1 and vdW-DF2).\footnote{Ji\v{r}\'{i} Klime\v{s} et al.\ , PRB 83, 195131 (2011) } \footnote{Kyuho Lee et al.\ , PRB 82, 081101(R) (2010) }Consistent with a physisorbed phase, binding energies and charge transfer per CF$_3$Cl molecule are calculated to be on the order of 280meV and 0.01e, respectively. By exploring different coverages and orientations of this ordered phase we are able to open a band gap in some configurations; said gap is in the range of 8 to 80meV depending on the strength of the effective pseudopotential. Furthermore, we calculate the screening of these effects in bi-layer and tri-layer graphene.