Topological insulator on the kagome lattice

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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 Z₂ 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.