Topological Insulators in Ternary Compounds with a Honeycomb Lattice

TL;DR

This paper investigates ternary compounds with honeycomb structures, revealing that LiAuSe is a topological insulator with a single Dirac cone, while KHgSb is topologically trivial, highlighting the role of spin-orbit coupling.

Contribution

It identifies specific ternary honeycomb compounds as topological insulators or trivial insulators based on their electronic structure and spin-orbit coupling effects.

Findings

LiAuSe is a topological non-trivial insulator.

KHgSb is a topologically trivial compound.

Surface states feature a single Dirac cone at the b3-point.

Abstract

One of the most exciting subjects in solid state physics is a single layer of graphite which exhibits a variety of unconventional novel properties. The key feature of its electronic structure are linear dispersive bands which cross in a single point at the Fermi energy. This so-called Dirac cone is closely related to the surface states of the recently discovered topological insulators. The ternary compounds, such as LiAuSe and KHgSb with a honeycomb structure of their Au-Se and Hg-Sb layers feature band inversion very similar to HgTe which is a strong precondition for existence of the topological surface states. In contrast to graphene with two Dirac cones at K and K' points, these materials exhibit the surface states formed by only a single Dirac cone at the \Gamma -point together with the small direct band gap opened by a strong spin-orbit coupling (SOC) in the bulk. These materials are centro-symmetric, therefore, it is possible to determine the parity of their wave functions, and hence, their topological character. Surprisingly, the compound KHgSb with the strong SOC is topologically trivial, whereas LiAuSe is found to be a topological non-trivial insulator.