1/4 is the new 1/2 when topology is intertwined with Mottness

TL;DR

This paper demonstrates that strong interactions can shift topological states from half-filling to quarter-filling, leading to a topological Mott insulator with potential ferromagnetism, explaining recent experimental observations.

Contribution

It reveals that interactions enable topological states at quarter-filling, extending the understanding of topology in strongly correlated systems beyond non-interacting models.

Findings

Topological states can occur at quarter-filling due to interactions.

A topological Mott insulator phase is identified in the model.

Possible ferromagnetic order at zero temperature is suggested.

Abstract

In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at $T=0$. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moire systems.