Fractional Quantum Hall states in strongly correlated multi-orbital systems

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 will discuss how orbital degrees of freedom in frustrated lattice systems lead to a narrowing of topologically nontrivial bands [1]. This robust effect does not rely on fine-tuned long-range hopping parameters and is directly relevant to a wide class of transition metal compounds. In addition, we will 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 [2]. On top of a self-consistent mean-field approach, we use exact diagonalization to study an effective one-band model for the emerging flat band in the presence of longer-range interactions and establish the signatures of a spontaneous $\nu = \frac{1}{3}$ FQH state. \\[4pt] [1] J. W.F. Venderbos, M. Daghofer, J. van den Brink, PRL {\bf 107}, 076405 (2011) \\[0pt] [2] J. W.F. Venderbos, S. Kourtis, J. van den Brink, M. Daghofer, arXiv:1109.5955