Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene

TL;DR

This paper demonstrates that isolated topological bands in twisted bilayer graphene can host nearly decoupled, non-local magnetic moments, leading to a Mott semimetal state with distinctive thermodynamic properties.

Contribution

It introduces a minimal analytic model showing the emergence of non-local moments in topological bands of TBG, bridging topology and Hubbard physics without extra degrees of freedom.

Findings

Model reproduces thermodynamic measurements of TBG.

Identifies a Mott semimetal phase at charge neutrality.

Predicts spectral imbalance and zero quasiparticle weight at Gamma.

Abstract

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 exhibits quantum anomalous Hall effects. On the other hand, these bands have concentrated charge density and show signs of extensive entropy resembling 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 states? In this work, we answer the question affirmatively by proposing 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. Importantly, charge concentration also leads to Berry curvature concentration at $\Gamma$, generating a small parameter $s$ that yields analytic tractability. We show that, rather surprisingly, the model hosts nearly decoupled flavor moments without any extra degrees of freedom. These moments are non-local due to topology-enforced power-law tails, yet have parametrically small overlap. We further develop a diagrammatic expansion in which the self energy can be computed exactly to leading order in $s^2$ in the fluctuating moment regime. At charge neutrality, we find a "Mott semimetal", with large flavor entropy and a Mott gap everywhere in the BZ except for the vicinity of the $\Gamma$ point. Away from neutrality, the Mott semimetal gaps out in a spectrally imbalanced manner, with one Mott band having zero $Z_k$ at the $\Gamma$ 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.