Interactions in the 8-orbital model for twisted bilayer graphene

TL;DR

This paper calculates the interaction parameters in an 8-orbital model for twisted bilayer graphene, emphasizing the dominance of density-density interactions and their decay, which influence the material's low-energy properties and response to doping.

Contribution

It provides detailed estimates of interaction strengths and screening effects in the 8-orbital model, highlighting the importance of density-density interactions over exchange and assisted-hopping terms.

Findings

Density-density interactions dominate the low-energy physics.

Interactions decay faster than in simpler models, following a 1/r law without gates.

Onsite interaction magnitude is about 40 meV, influenced by AA region size.

Abstract

We calculate the interactions between the Wannier functions of the 8-orbital model for twisted bilayer graphene (TBG). In this model, two orbitals per valley centered at the AA regions, the AA-p orbitals, account for the most part of the spectral weight of the flats bands. Exchange and assisted-hopping terms between these orbitals are found to be small. Therefore, the low energy properties of TBG will be determined by the density-density interactions. These interactions decay with the distance much faster than in the two orbital model, following a 1/r law in the absence of gates. The magnitude of the largest interaction in the model, the onsite term between the flat band orbitals, is controlled by the size of the AA regions and is estimated to be ~ 40 meV. To screen this interaction, the metallic gates have to be placed at a distance smaller than 5 nm. For larger distances only the long-range part of the interaction is substantially screened. The model reproduces the band deformation induced by doping found in other approaches within the Hartree approximation. Such deformation reveals the presence of other orbitals in the flat bands and is sensitive to the inclusion of the interactions involving them.