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

Abstract

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 non-trivial topological invariants (Chern number or $Z_2$ 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 non-interacting limit. We present comprehensive mean-field phase diagrams for these lattices and discuss the competition between topologically non-trivial phases and numerous other ordered states, including various charge, spin, and bond orderings. Our results suggest that $Z_2$ topological insulators should be found in a number of systems with either little or no intrinsic spin-orbit coupling.

16 pages, 12 figures

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• Electronic structure of (LaNiO${}_3$)${}_2$/(LaAlO${}_3$)${}_N$ heterostructures grown along [111]
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• Electron Correlation Induced Spontaneous Symmetry Breaking and Weyl Semimetal Phase in a Strongly Spin-Orbit Coupled System
• Topological Phases in Oxide Heterostructures with Light and Heavy Transition Metal Ions
• Electron Correlation Effects on Topological Phases
• Temperature-induced spontaneous time-reversal symmetry breaking on the honeycomb lattice
• Spontaneous loop-spin current with topological characters in the Hubbard model