Topological Phases in Triangular Lattices of Ru Adsorbed on Graphene:   ab-initio calculations
  We have performed an ab initio investigation of the electronic properties of the graphene sheet adsorbed by Ru adatoms (Ru/graphene). For a particular set of triangular arrays of Ru adatoms, we find the formation of four (spin-polarized) Dirac cones attributed to a suitable overlap between two hexagonal lattices: one composed by the C sites of the graphene sheet, and the other formed by the surface potential induced by the Ru adatoms. Upon the presence of spin-orbit coupling (SOC) nontrivial band gaps take place at the Dirac cones promoting several topological phases. Depending on the Ru concentration, the system can be topologically characterized among the phases i) Quantum Spin Hall (QSH), ii) Quantum Anomalous Hall (QAH), iii) metal iv) or trivial insulator. For each concentration, the topological phase is characterized by the ab-initio calculation of the Chern number. 
C. Mera Acosta, Matheus P. Lima, R. H. Miwa, Antonio J. R. da Silva,   A. Fazzio
cond-mat.mes-hall