Fractional Chern insulator on a triangular lattice of strongly correlated $t_{2g}$ electrons

TL;DR

This paper explores the emergence and robustness of fractional Chern insulators in a triangular lattice model with strongly correlated $t_{2g}$ electrons, revealing conditions for their stability and competition with charge density waves.

Contribution

It demonstrates the realization of fractional Chern insulators in a realistic multi-orbital model and analyzes their stability against disorder and competing phases.

Findings

FCIs appear at various fillings with signatures like fractional statistics.

FCIs are robust against disorder and do not require extremely flat bands.

Weaker interactions can induce FCIs in less flat bands.

Abstract

We discuss the low-energy limit of three-orbital Kondo-lattice and Hubbard models describing $t_{2g}$ orbitals on a triangular lattice near half-filling. We analyze how very flat bands with non-trivial topological character, a Chern number C=1, arise both in the limit of infinite on-site interactions as well as in more realistic regimes. Exact diagonalization is then used to investigate fractional filling of an effective one-band spinless-fermion model including nearest-neighbor interaction $V$; it reveals signatures of fractional Chern insulators (FCIs) for several filling fractions. In addition to indications based on energies, e.g. flux insertion and fractional statistics of quasiholes, Chern numbers are obtained. It is shown that FCIs are robust against disorder in the underlying magnetic texture that defines the topological character of the band. We also investigate competition between FCI states and a charge density wave (CDW) and discuss particle-hole asymmetry as well as Fermi-surface nesting. FCI states turn out to be rather robust and do not require very flat bands, but can also arise when filling or an absence of Fermi-surface nesting disfavor the competing CDW. Nevertheless, very flat bands allow FCI states to be induced by weaker interactions than those needed for more dispersive bands.