Topological states of non-Dirac electrons on Si[111] surface

In the present work, we demonstrate the possibility of nontrivial topology of non-Dirac electrons. In particular, we show that, in two dimensional systems with $C_{\rm 3}$ crystal symmetry and time reversal symmetry, multiple $p$-orbits exhibit a degeneracy and quadratic non-Dirac band dispersions at $\Gamma$ point. When the atomic spin-orbit coupling (SOC) is taken into account, a gap is opend at $\Gamma$ point and a quantum spin Hall effect state is realized. We construct a $k\cdot p$ model to reveal the nontrivial topology which is associated with a meron structure with double vorticity in the pseudo spin texture, a mechanism different from that on honeycomb lattice and the band inversion. We propose that Si[111] surface with 1/3 regular coverage of Bi atoms is a realization of our idea. First-principles calculations show that this system takes a quantum spin Hall phase with topological gap as large as $\sim 0.15$eV.