Nonlocal Moments and Dirac Trions in the Concentrated Chern Bands of Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: quantum Hall physics and Hubbard physics. On one hand, TBG hosts flat topological Landau-level-like bands which exhibit quantum anomalous Hall effects. On the other hand, these bands have concentrated charge density and show signs of extensive entropy. We study a minimal model for these bands in TBG that combines topology and charge concentration at the AA sites, leading to analytic wavefunctions that closely approximate those of the BM model with realistic parameters. Charge concentration also leads to Berry curvature concentration at Γ, generating a small parameter "s" that yields analytic tractability. The model hosts "nonlocal" flavor moments with topology enforced power law tails and parametrically small Curie temperature. 

The fluctuating nonlocal moments lead to "Mott Semimetal" at charge neutrality, with large flavor entropy and a Mott gap everywhere in the BZ except for the vicinity of the Γ point. Away from neutrality, the Mott semimetal gaps out in a spectrally imbalanced manner, with one Mott band having zero spectral weight at the Γ point. We show that the missing spectral weight corresponds to a trion excitation, specifically a hole combined with a density wave. Despite being composed of heavy particles away from the Γ point, the trion can have arbitrarily small mass. We find that the charge carriers in the normal state of the TBG superconductor are almost entirely trionic near ν=−2.