Electronic Instabilities of the AA-Honeycomb Bilayer

TL;DR

This study employs a functional renormalization group approach to analyze electron-electron interaction-induced instabilities in AA-stacked bilayer honeycomb lattices, revealing various phases influenced by interaction range and comparing with other graphene structures.

Contribution

It provides a detailed phase diagram for AA-stacked bilayer graphene considering local and nonlocal interactions, extending understanding beyond single-layer and AB-stacked bilayer graphene.

Findings

Antiferromagnetic spin-density wave as a dominant instability with local repulsion.

Presence of other instabilities due to nonlocal interactions.

Comparison of phase diagrams with single-layer and AB-stacked bilayer graphene.

Abstract

We use a functional renormalization group approach to study the instabilities due to electron-electron interactions in a bilayer honeycomb lattice model with AA stacking, as it might be relevant for layered graphene with this structure. Starting with a tight- binding description for the four $\pi$-bands, we integrate out the modes of the dispersion by successively lowering an infrared cutoff and determine the leading tendencies in the effective interactions. The antiferromagnetic spin-density wave is an expected instability for dominant local repulsion among the electrons, but for nonlocal interaction terms also other instabilities occur. We discuss the phase diagrams depending on the model parameters. We compare our results to single-layer graphene and the more common AB-stacked bilayer, both qualitatively and quantitatively.