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

TL;DR

This paper investigates the interplay of correlations, magnetism, and superconductivity in a two-orbital honeycomb lattice model inspired by twisted bilayer graphene, revealing complex phases and instabilities through strong-coupling analysis.

Contribution

It introduces a comprehensive strong-coupling analysis of a two-orbital Hubbard model on the honeycomb lattice, exploring superconducting, magnetic, and charge phases relevant to twisted bilayer graphene.

Findings

Identification of various superconducting and magnetic instabilities.

Discovery of nematic and chiral vestigial phases in pairing channels.

Rich interplay between magnetic orders and orbital nematicity.

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 $\left(p_{x},\,p_{y}\right)$ 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 ($d$-wave) pairing channels, which admit vestigial phases with nematic or chiral orders, and study their phenomenology. Furthermore, we explore the strong-regime by obtaining a simplified spin-orbital exchange model which may describe a putative Mott-like insulating state at quarter-filling. Our mean-field solution reveals a rich intertwinement between ferro- and antiferro-magnetic 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.