The nature of correlations in the insulating states of twisted bilayer graphene

TL;DR

This paper investigates the insulating states in twisted bilayer graphene, showing that non-local correlations are essential to accurately describe experimental observations and challenge the traditional local correlation models.

Contribution

It demonstrates that including inter-site correlations in the Hubbard model aligns theoretical predictions with experimental data for twisted bilayer graphene's insulating states.

Findings

Non-local correlations are crucial for accurate modeling.

Experimental temperature and magnetic field dependencies are explained.

Antiferromagnetic correlations influence the Mott transition.

Abstract

The recently observed superconductivity in twisted bilayer graphene emerges from insulating states believed to arise from electronic correlations. While there have been many proposals to explain the insulating behaviour, the commensurability at which these states appear suggests that they are Mott insulators. Here we focus on the insulating states with $\pm 2$ electrons or holes with respect to the charge neutrality point. We show that the theoretical expectations for the Mott insulating states are not compatible with the experimentally observed dependence on temperature and magnetic field if, as frequently assumed, only the correlations between electrons on the same site are included. We argue that the inclusion of non-local (inter-site) correlations in the treatment of the Hubbard model can bring the predictions for the magnetic and temperature dependencies of the Mott transition to an agreement with experiments and have consequences for the critical interactions, the size of the gap, and possible pseudogap physics. The importance of the inter-site correlations to explain the experimental observations indicates that the observed insulating gap is not the one between the Hubbard bands and that antiferromagnetic-like correlations play a key role in the Mott transition.