Density waves and Cooper pairing on the honeycomb lattice

TL;DR

This paper explores electron instabilities on the honeycomb lattice, revealing how interactions lead to various ordered states and pairing mechanisms, especially near and away from half-filling, using a renormalization group approach.

Contribution

It provides new insights into the emergence of pairing and density-wave instabilities on the honeycomb lattice with onsite and nearest-neighbor interactions.

Findings

Critical interaction strengths needed for antiferromagnetic and charge-density wave orders near half-filling.

Emergence of f-wave triplet and d+id singlet pairing instabilities away from half-filling.

Density-wave regimes serve as precursors to pairing instabilities.

Abstract

Motivated by the surge in research activities on graphene, we investigate instabilities of electrons on the honeycomb lattice, interacting by onsite and nearest-neighbor terms, using a renormalization group scheme. Near half band-filling, critical minimal interaction strengths are required for instabilities toward antiferromagnetic or charge-density wave order. Away from half filling, f-wave triplet pairing and d+id singlet pairing instabilities are found to emerge out of density-wave regimes.