Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions

TL;DR

This paper explores the nature of correlated insulating states in magic-angle twisted bilayer graphene, highlighting the importance of competing interactions and proposing two potential insulating states with implications for superconductivity.

Contribution

It introduces a realistic extended Hubbard model considering overlapping Wannier orbitals and identifies two candidate insulating states, advancing understanding of TBG's correlated phases.

Findings

Proposes spin- and valley-ferromagnetic band insulator as a candidate state.

Suggests Dirac semimetallic state with van Hove singularity influences superconductivity.

Aligns theoretical degeneracy with experimental Landau level observations.

Abstract

We investigate correlated insulating states in magic-angle twisted bilayer graphene (TBG) by the exact diagonalization method applied to the extended Hubbard model with interaction parameters recently evaluated in the realistic effective model. Our model can handle the competing interactions among Wannier orbitals owing to their significant overlap, which is a crucial but overlooked aspect of the magic-angle TBG. We propose two candidates for the correlated insulating states: spin- and valley-ferromagnetic band insulator and the Dirac semimetallic state for two flavors with peculiar renormalization, where a flavor denotes a combined degree of freedom with spin and valley. One of the important consequences for the latter candidate is that it allows van Hove singularity near half-filling of the whole band structure (i.e. near the Dirac points) to play some role in superconductivity. The consistency between the two flavor degrees of freedom for the Dirac semimetallic state and the two-fold degeneracy of the Landau level observed in the experiment is also noteworthy.