Topological insulator on the kagome lattice

TL;DR

This paper explores how breaking symmetries in a Kagome lattice with itinerant electrons can lead to various topological and trivial insulating phases, including topological insulators and Kekule phases with fractional excitations.

Contribution

It introduces new topological and trivial insulating phases in the Kagome lattice induced by symmetry-breaking perturbations, highlighting the emergence of fractionalized excitations.

Findings

Identification of a 2D topological insulator with robust edge states

Discovery of Kekule insulators with fractional charge vortices

Charge density wave coupling as an axial gauge field

Abstract

Itinerant electrons in a two-dimensional Kagome lattice form a Dirac semi-metal, similar to graphene. When lattice and spin symmetries are broken by various periodic perturbations this semi-metal is shown to spawn interesting non-magnetic insulating phases. These include a two-dimensional topological insulator with a non-trivial Z_2 invariant and robust gapless edge states, as well as dimerized and trimerized `Kekule' insulators. The latter two are topologically trivial but the Kekule phase possesses a complex order parameter with fractionally charged vortex excitations. A charge density wave is shown to couple to the Dirac fermions as an effective axial gauge field.