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

## TL;DR

This paper introduces a three-band Hubbard model that unifies topological insulator behavior, zigzag antiferromagnetism, and Kitaev-Heisenberg physics in Na$_2$IrO$_3$, reconciling experimental observations with theoretical models.

## Contribution

It proposes a comprehensive three-band Hubbard model that captures multiple phases of Na$_2$IrO$_3$, including topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg regimes.

## Key findings

- Unifies topological insulator and magnetic phases within a single model.
- Shows charge fluctuations can explain zigzag antiferromagnetism.
- Identifies interaction strength regimes for different phases.

## 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.