Topological insulator on the kagome lattice

Itinerant electrons in a two-dimensional kagome lattice form a Dirac semimetal, similar to graphene. When lattice and spin symmetries are broken by various periodic perturbations this semimetal is shown to spawn interesting nonmagnetic insulating phases. These include a two-dimensional topological insulator with a nontrivial Z₂ invariant and robust gapless edge states, as well as dimerized and trimerized ``Kekul\'e'' insulators. The latter two are topologically trivial but the Kekul\'e 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.