Narrowing of topological bands due to electronic orbital degrees of freedom

The Fractional Quantum Hall (FQH) effect has been predicted to occur in absence of magnetic fields and at high temperature in lattice systems that have flat bands with non-zero Chern number. We demonstrate that the presence of orbital degrees of freedom in frustrated lattice systems leads to a narrowing of topologically nontrivial bands. This robust effect does not rely on a fine-tuning of long-range hopping parameters as do other recent proposals to realize lattice FQH states and is directly relevant to a wide class of transition metal compounds.