Fractional quantum-Hall liquid spontaneously generated by strongly correlated t_2g electrons

TL;DR

This paper demonstrates that strongly correlated t_2g electrons on a triangular lattice can spontaneously generate a fractional quantum-Hall state through magnetic ordering, without external magnetic fields, and confirms this with exact diagonalization.

Contribution

It reveals a robust mechanism where electron correlations induce topologically nontrivial bands and a spontaneous FQH state in a t_2g system, going beyond mean field approximations.

Findings

Formation of spin-chiral magnetic order induces topologically nontrivial flat bands.

Exact diagonalization confirms signatures of a spontaneous FQH state.

The behavior is robust and does not require fine tuning.

Abstract

For topologically nontrivial and very narrow bands, Coulomb repulsion between electrons has been predicted to give rise to a spontaneous fractional quantum-Hall (FQH) state in absence of magnetic fields. Here we show that strongly correlated electrons in a t_2g-orbital system on a triangular lattice self-organize into a spin-chiral magnetic ordering pattern that induces precisely the required topologically nontrivial and flat bands. This behavior is very robust and does not rely on fine tuning. In order to go beyond mean field and to study the impact of longer-range interactions, we map the low-energy electronic states onto an effective one-band model. Exact diagonalization is then used to establish signatures of a spontaneous FQH state.