Recipe for higher-order topology on the triangular lattice

TL;DR

This paper proposes a method to realize higher-order topological insulators on the triangular lattice by breaking mirror symmetry, identifying material platforms like certain monolayers on SiC substrates.

Contribution

It introduces a recipe for HOTIs on the triangular lattice, highlighting the role of mirror symmetry breaking and spin-orbit coupling in phase determination.

Findings

HOTIs can be realized without spin-orbit coupling.

Triangular monolayer adsorbates on SiC are predicted as ideal platforms.

Four topologically distinct phases identified based on symmetry and spin-orbit interactions.

Abstract

We present a recipe for an electronic 2D higher order topological insulator (HOTI) on the 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 $X=$(Al,B,Ga) on SiC.