Instabilities of interacting electrons on the honeycomb bilayer

TL;DR

This paper uses functional renormalization group analysis to explore electron interaction instabilities in honeycomb bilayer systems, revealing a new gapless charge-density wave and proximity to magnetic and topological phases, with implications for real graphene.

Contribution

It introduces a novel gapless charge-density wave instability and assesses the effects of realistic interactions and doping on phase boundaries in honeycomb bilayer systems.

Findings

Discovery of a gapless charge-density wave instability.

Proximity of the system to antiferromagnetic and quantum spin Hall phases.

Large energy scales for instabilities suggest real-world effects are sensitive to imperfections.

Abstract

We investigate the instabilities of interacting electrons on the honeycomb bilayer by means of the functional renormalization group for a range of interactions up to the third-nearest neighbor. Besides a novel instability toward a gapless charge-density wave we find that using interaction parameters as determined by ab-initio calculations for graphene and graphite puts the system close to the boundary between antiferromagnetic and quantum spin Hall instabilities. Importantly, the energy scales for these instabilities are large such that imperfections and deviations from the basic model are expected to play a major role in real bilayer graphene, where interaction effects seem to be seen only at smaller scales. We therefore analyze how reducing the critical scale and small doping of the layers affect the instabilities.