Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices

We study the spinless and spinful extended Hubbard models with repulsive interactions on the kagome and the decorated honeycomb (star) lattice. Using Hartree-Fock mean-field theory, we show that interaction-driven insulating phases with nontrivial topological invariants (Chern number or Z2 invariant) exist for an experimentally reasonable range of parameters. These phases occur at filling fractions which involve either Dirac points or quadratic band crossing points in the noninteracting limit. We present comprehensive mean-field phase diagrams for these lattices and discuss the competition between topologically nontrivial phases and numerous other ordered states, including various charge, spin, and bond orderings. Our results suggest that Z₂ topological insulators should be found in a number of systems with either little or no intrinsic spin-orbit coupling.