Recipe for higher order topology on the triangular lattice

Abstract

We present a recipe for an electronic two-dimensional (2D) higher order topological insulator (HOTI) on a triangular lattice that can be realized in a large family of materials. The essential ingredient is mirror symmetry breaking, which allows for a finite quadrupole moment and trivial ${\mathbb{Z}}_{2}$ index. The competition between spin-orbit coupling and the symmetry-breaking terms gives rise to four topologically distinct phases; the HOTI phase appears when symmetry breaking dominates, including in the absence of spin-orbit coupling. We identify triangular monolayer adsorbate systems on the (111) surface of zincblende/diamond type substrates as ideal material platforms and predict the HOTI phase for $X=(\mathrm{Al},\mathrm{B},\mathrm{Ga})$ on SiC.