Topological states of non-Dirac electrons on triangular lattice

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We demonstrate the possibility of topological states for non-Dirac electrons. Specifically it is shown that, because of the C 3 crystal symmetry and time reversal symmetry, pₓ and py orbits accommodated on triangular lattice exhibit a quadratic band touching at Γ point at the Fermi level. When the atomic spin-orbit coupling (SOC) is taken into account, a gap is opened resulting in a quantum spin Hall effect state. As revealed explicitly by a k· p model, the topology is associated with a meron structure in the pseudo spin texture with vorticity two, a mechanism different from honeycomb lattice and the band inversion. One possible realization of this scheme is the 1/3 coverage by Bi atom adapted on the Si[111] surface. First-principle calculations are carried out, and a global gap of 0.15eV is observed. With the Si substrate taking part in realizing the nontrivial topology, the present template is expected to make the integration of topological states into existing electronics and photonics technologies promising.