Supplemental Material for “ Giant topological insulator gap in graphene with 5 d adatoms ”

The tight-binding model studied in the main text preserves (three-dimensional) inversion symmetry about an adatom site, which sends crα → c−rα and fmRα → −fm−Rα. Thus one can simultaneously diagonalize the Hamiltonian and the operator R implementing this transformation. Fu and Kane [1] showed that the Z2 invariant can be deduced very simply from the inversion eigenvalues of energy eigenstates at the four time-reversal-invariant momenta Pj that satisfy Pj = −Pj up to a reciprocal lattice vector. For the 4 × 4 supercell considered in the main text these momenta are P1 = (0, 0) at the zone center and P2 = (0, π 23 ), P3 = ( π 4 , π 4 √ 3 ), and P4 = (π4 ,− π 4 √ 3 ) at the midpoints of the zone edges (here we have set the lattice constant to unity).