Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands

We consider the core problem of Coulomb interactions within fractionally filled Moiré flat bands and demonstrate that the dual description in terms of holes, which acquire a non-trivial hole-dispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. We find that the single-hole dispersion has a profound impact on the phase diagram: in experimentally relevant examples such as ABC stacked trilayer and twisted bilayer graphene aligned with boron nitride, it leads to emergent Fermi liquid states at band filling fractions down to 1/3 and 2/3 respectively. At even lower filling fractions, the electron density still faithfully tracks the single-hole dispersion while exhibiting distinct non-Fermi liquid behaviour. We also show that fractional Chern insulators can form in twisted bilayer graphene aligned with boron nitride at band filling 1/3.