Charge order and antiferromagnetism in twisted bilayer graphene from the variational cluster approximation

TL;DR

This study investigates charge order and antiferromagnetism in twisted bilayer graphene using the variational cluster approximation, revealing correlated insulating states and conditions for magnetic order at specific fillings.

Contribution

It extends a model of twisted bilayer graphene by including extended interactions and applies a variational cluster approach to analyze charge and magnetic orders.

Findings

Correlated Mott insulators at quarter, half, and three-quarter fillings.

No charge order at quarter filling across tested interactions.

Antiferromagnetism at half-filling requires large local repulsion U.

Abstract

We study the possibility of charge order at quarter filling and antiferromagnetism at half-filling in a tight-binding model of magic angle twisted bilayer graphene. We build on the model proposed by Kang and Vafek [Physical Review X 8(3), 031088 (2018)], relevant to a twist angle of $1.30^\circ$, and add on-site and extended density-density interactions. Applying the variational cluster approximation with an exact-diagonalization impurity solver, we find that the system is indeed a correlated (Mott) insulator at fillings $\frac14$, $\frac12$ and $\frac34$. At quarter filling, we check that the most probable charge orders do not arise, for all values of the interaction tested. At half-filling, antiferromagnetism only arises if the local repulsion $U$ is sufficiently large compared to the extended interactions, beyond what is expected from the simplest model of extended interactions.