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. 

We show that orbital degrees of freedom in frustrated lattice systems leads to a narrowing of topologically nontrivial bands for robust parameter ranges. 

We find that a strongly correlated $t_$ system on a triangular lattice can support a spin-chiral magnetic ordering pattern with such topologically nontrivial and flat bands. 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. 

J. W. F. Venderbos, M. Daghofer and J. van den Brink, Phys. Rev. Lett. 107, 116401 (2011);
J. W. F. Venderbos, S. Kourtis, J. van den Brink and M. Daghofer, Phys. Rev. Lett. 108, 126405 (2012).