Nonlocal Moments and Mott Semimetal in the 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 the quantum anomalous Hall effects under the right conditions. On the other hand, these bands are characterized by concentrated charge density and show signs of extensive entropy usually attributed to local moments. The combination of these features leads to a question: Can decoupled moments emerge in an isolated topological band, despite the lack of exponentially localized Wannier orbitals? In this work, we answer the question affirmatively by proposing a minimal model for the flat topological bands in TBG that combines topology and charge concentration at the AA sites, leading to analytic wave functions that closely approximate those of the Bistritzer-MacDonald model with realistic parameters. Importantly, charge concentration also leads to Berry curvature concentration at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Γ</a:mi></a:math>, giving rise to a small parameter <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>s</d:mi></d:math> that makes the model analytically tractable. We show that, rather surprisingly, the model hosts nearly decoupled flavor moments without invoking any extra degrees of freedom. These moments are nonlocal due to topology-enforced power-law tails, yet have parametrically small overlap. We develop a systematic diagrammatic expansion in which the self-energy can be computed exactly to leading order in <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msup><f:mi>s</f:mi><f:mn>2</f:mn></f:msup></f:math> in the fluctuating moment regime and predict momentum-resolved spectral functions for future experiments to verify. Our key discovery is a charge-neutrality state we refer to as the “Mott semimetal” characterized by high flavor entropy and a Mott gap that exists throughout most of the Brillouin zone but closes at the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="normal">Γ</h:mi></h:math> point. At <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="normal">Γ</k:mi></k:math>, the spectral function contains a single Dirac cone per spin per valley and responds to perturbations in an exotic manner that is distinct from any other theoretical picture of TBG. Away from neutrality, the Mott semimetal gaps out in a spectrally imbalanced manner, with one Mott band having zero quasiparticle residue at the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi mathvariant="normal">Γ</n:mi></n:math> point. The model accurately reproduces results from finite-temperature thermodynamic measurements, leads to new experimental predictions, and resolves the problem of the emergence of Hubbard physics in isolated topological bands.