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We study the spinless and spinful extended Hubbard models with repulsiveinteractions on the kagome and the decorated honeycomb ("star") lattice. UsingHartree-Fock mean-field theory, we show that interaction-driven insulatingphases with non-trivial topological invariants (Chern number or $Z_2$invariant) exist for an experimentally reasonable range of parameters. Thesephases occur at filling fractions which involve either Dirac points orquadratic band crossing points in the non-interacting limit. We presentcomprehensive mean-field phase diagrams for these lattices and discuss thecompetition between topologically non-trivial phases and numerous other orderedstates, including various charge, spin, and bond orderings. Our results suggestthat $Z_2$ topological insulators should be found in a number of systems witheither little or no intrinsic spin-orbit coupling.

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