Fractional Chern insulator states in an isolated flat band of zero Chern number

A flat band with Chern number C=0, and well isolated from the rest of Hilbert space by a gap much larger than interaction strength, is a context that has not been regarded as relevant for fractional quantum Hall physics. In this work, we demonstrate the emergence of the fractional Chern insulator (FCI) states in such a trivial flat band, using large-scale exact diagonalization (ED) and infinite density matrix renormalization group (iDMRG) simulations. The C=0 isolated flat band is hosted by an anisotropic fluxed dice lattice. Both the quantum metric and Berry curvature of the C=0 flat band have a sharp peak at the Γ point, whereas in the rest of the Brillouin zone (BZ) they mimic the quantum geometry of the lowest Landau level. We consider nearest-neighbor repulsion that is weak enough to ensure the isolated-band limit is always satisfied. From the projected ED simulations at νF=2/3 electron filling of the flat band (i. e. 1/3 hole filling), we find the unexpected FCI with 3-fold ground-state degeneracy and σH=-1/3 (e²/h). The momentum space carrier distribution shows that the quantum metric peak tends to push the interacting holes away from Γ point towards the BZ regions with the nearly ``ideal'' quantum geometry, underlying the formation of FCI in the C=0 flat band. Besides, when tuning the single-particle anisotropy such that the quantum geometry of the C=0 flat band becomes less sharp around Γ, we find the ground state becomes a charge density wave with tripled unit cell at νF=2/3. Our two-band iDMRG simulations further corroborate the FCI in the isolated C=0 flat band, demonstrating in such parameter regime the fractionally quantized charge pumping upon flux insertion as well as the momentum-resolved entanglement spectrum characteristic of the 1/3 Laughlin state.