Chern-insulator phases and spontaneous spin and valley order in a moir\'e lattice model for magic-angle twisted bilayer graphene

TL;DR

This study uses self-consistent Hartree-Fock calculations on a moiré lattice model to explore topological phases and spontaneous order in magic-angle twisted bilayer graphene, revealing interaction-driven Chern insulators and metallic phases.

Contribution

It provides a detailed phase diagram showing how Coulomb interactions induce topological and magnetic orders across different fillings in twisted bilayer graphene.

Findings

Presence of quantum valley Hall phase at all integer fillings with strong interactions.

Emergence of Chern-insulator phases with spontaneous spin/valley polarization at nonzero fillings.

Existence of metallic inhomogeneous spin/valley ordered phases at weaker interactions.

Abstract

At a certain "magic" relative twist angle of two graphene sheets it remains a challenge to obtain a detailed description of the proliferation of correlated topological electronic phases and their filling-dependence. We perform a self-consistent real-space Hartree-Fock study of an effective moir{\'e} lattice model to map out the preferred ordered phases as a function of Coulomb interaction strength and moir{\'e} flat-band filling factor. It is found that a quantum valley Hall phase, previously discovered at charge neutrality, is present at all integer fillings for sufficiently large interactions. However, except from charge neutrality additional spontaneous spin/valley polarization is present in the ground state at nonzero integer fillings, leading to Chern-insulator phases and anomalous quantum Hall effects at odd filling factors, thus constituting an example of interaction-driven nontrivial topology. At weaker interactions, all nonzero integer fillings feature metallic inhomogeneous spin/valley ordered phases which may also break additional point group symmetries of the system. We discuss these findings in the light of previous theoretical studies and recent experimental developments of magic-angle twisted bilayer graphene.