Three-band Hubbard model for Na${}_2$IrO${}_3$: Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material

Abstract

Na${}_2$IrO${}_3$ was one of the first materials proposed to feature the Kane-Mele type topological insulator phase. Contemporaneously it was claimed that the very same material is in a Mott insulating phase which is described by the Kitaev-Heisenberg (KH) model. First experiments indeed revealed Mott insulating behavior in conjunction with antiferromagnetic long-range order. Further refined experiments established antiferromagnetic order of zigzag type which is not captured by the KH model. Since then several extensions and modifications of the KH model were proposed in order to describe the experimental findings. Here we suggest that adding charge fluctuations to the KH model represents an alternative explanation of zigzag antiferromagnetism. Moreover, a phenomenological three-band Hubbard model unifies all the pieces of the puzzle: topological insulator physics for weak and KH model for strong electron-electron interactions as well as a zigzag antiferromagnet at intermediate interaction strength.

5 pages, 3 figures; v2 (as published): added discussion about kinetic energy scale C; more realistic values of C shift the zigzag AFM phase to larger values of U

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• Dominant Kitaev interactions in the honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Multiloop functional renormalization group approach to quantum spin systems
• Spin-orbit coupled systems in the "atomic" limit: rhenates, osmates, iridates
• Model Hamiltonian for strongly-correlated systems: Systematic, self-consistent, and unique construction
• Spin waves and stability of zigzag order in the Hubbard model with spin-dependent hopping terms - Application to the honeycomb lattice compounds $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$ and $\alpha -\mathrm{RuC}{\mathrm{l}}_3$
• Kinetic Ferromagnetism and Topological Magnons of the Hole-Doped Kitaev Spin Liquid
• Topological property of a $t_{2g}^5$ system with a honeycomb lattice structure
• Conductivity of Dirac-like surface states in correlated honeycomb transition metal oxide Mott insulators
• Phase diagram of the Kitaev-Hubbard model: ${\mathbb{Z}}_2$ slave-spin and QMC approaches