Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene

Abstract

The recent observation of superconductivity in proximity to an insulating phase in twisted bilayer graphene (TBG) at small ``magic'' twist angles has been linked to the existence of nearly flat bands, which make TBG a fresh playground to investigate the interplay between correlations and superconductivity. The low-energy narrow bands were shown to be well described by an effective tight-binding model on the honeycomb lattice (the dual of the triangular Moir\'e superlattice) with a local orbital degree of freedom. In this paper, we perform a strong-coupling analysis of the proposed $\left({p}_{x},\phantom{\rule{0.16em}{0ex}}{p}_{y}\right)$ two-orbital extended Hubbard model on the honeycomb lattice. By decomposing the interacting terms in the particle-particle and particle-hole channels, we classify the different possible superconducting, magnetic, and charge instabilities of the system. In the pairing case, we pay particular attention to the two-component ($d\text{\ensuremath{-}}\mathrm{wave}$) pairing channels, which admit vestigial phases with nematic or chiral orders, and study their phenomenology. Furthermore, we explore the strong-coupling regime by obtaining a simplified spin-orbital exchange model which may describe a putative Mott-type insulating state at quarter-filling. Our mean-field solution reveals a rich intertwinement between ferromagnetic and antiferromagnetic orders with different types of nematic and magnetic orbital orders. Overall, our work provides a solid framework for further investigations of the phase diagram of the two-orbital extended Hubbard model in both strong- and weak-coupling regimes.