Quantum Geometry and Stability of Fractional Chern Insulators II: Multiband Formulation

Fractional Chern insulators (FCIs) are brought to a vast interest following their recent experimental discovery. Flat bands and ideal quantum geometry are believed to be the key requirements on the non-interacting band structure that allow for stable FCI states upon turning on the interaction. While most existing numerical simulations of FCI and competing many-body states work within the space of a single non-interacting band, some studies have also revealed the significance of interaction-induced band mixing effect. Here we perform combined exact diagonalization and Hartree-Fock simulations on a general setting of C6-symmetric Aharonov-Casher band subject to a periodic potential, which has been shown to well describe the physics of twisted transition metal dichalcogenide (TMD) homobilayers. We argue that the stability of FCI states at fractional filling factors can be closely related to the bandwidth and quantum geometry of the mean-field band at the nearest integer filling, which may account for the presence of FCI states in twisted TMD homobilayers at hole filling factor 2/3 rather than 1/3.