Topological states of non-Dirac electrons on a triangular lattice

We demonstrate possible nontrivial topology of non-Dirac electrons. In particular we show that, because of the C₃ crystal symmetry and time-reversal symmetry, multiple p orbitals accommodated on a triangular lattice exhibit a degeneracy and quadratic non-Dirac band dispersions at the Γ point. When the atomic spin-orbit coupling (SOC) is taken into account, a quantum spin Hall effect state is realized. As revealed explicitly by a k .p model, the nontrivial topology is associated with a meron structure with double vorticity in the pseudospin texture, a mechanism different from that on honeycomb lattice and the band inversion. One possible realization of this scheme is the Si[111] surface adapted by heavy elements with strong atomic SOC, with symmetry and orbitals selected by choosing coverage and auxiliary elements. In terms of first-principles calculations on 1/3 regular coverage of Bi a topological gap of ∼0.15 eV is derived.