Topological Anderson insulating phases in the interacting Haldane model

We analyze the influence of disorder and strong correlations on the topology of two-dimensional Chern insulators. A mean-field calculation in the half-filled Haldane model with extended Hubbard interactions and Anderson disorder shows that the disorder favors topology in the interacting case and extends the topological phase to a larger region of the Hubbard parameters. In the absence of a staggered potential, we find a novel disorder-driven topological phase with Chern number $C=1$, with the coexistence of topology with long-range spin and charge orders. More conventional topological Anderson insulating phases are also found in the presence of a finite staggered potential.