Topological phases induced by interactions and spin-orbit coupling in decorated honeycomb lattices

The decorated honeycomb lattice (DHL) is a playground to study non-interacting topological states of matter such as the quantum spin Hall (QSH) insulator due to its peculiar band structure containing flat bands, Dirac and quadratic band touching points. In the search of novel interacting topological states we have analyzed the interplay of spin-orbit coupling (SOC) and on-site Coulomb interaction based on a Kane-Mele-Hubbard model on the DHL. For weak Coulomb repulsion a transition from a QSH insulator to a non-trivial semimetal with a non-quantized spin Hall conductivity occurs as SOC is increased. In the strong interacting limit, SOC induces a transition from a resonance valence bond (RVB) spin liquid state to a magnetic insulator consisting of antiferromagnetically ordered S=3/2 localized moments on the honeycomb lattice. Our results are discussed in the context of organometallic compounds realizing the DHL.

[1] M. F. López and J. Merino, Phys. Rev. B 102, 035157 (2020).