Topological states of non-Dirac electrons on triangular lattice

TL;DR

This paper explores topological states in non-Dirac electrons on a triangular lattice, revealing a quantum spin Hall effect driven by spin-orbit coupling and a unique meron spin texture, with potential applications in electronics.

Contribution

It introduces a novel topological mechanism for non-Dirac electrons on a triangular lattice, distinct from honeycomb systems, and demonstrates its realization via first-principles calculations.

Findings

Quadratic band touching at the Gamma point due to C3 symmetry.

Spin-orbit coupling opens a gap leading to quantum spin Hall state.

Global gap of approximately 0.15 eV observed in calculations.

Abstract

We demonstrate the possibility of topological states for non-Dirac electrons. Specifically it is shown that, because of the $C_{\rm 3}$ crystal symmetry and time reversal symmetry, $p_x$ and $p_y$ orbits accommodated on triangular lattice exhibit a quadratic band touching at $\Gamma$ 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 $k\cdot p$ 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 $\sim 0.15$eV 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.