Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling

TL;DR

This paper investigates the competing electronic orders in doped honeycomb lattices near van Hove singularities using a functional renormalization group approach, revealing various superconducting and magnetic phases influenced by exchange and Coulomb interactions.

Contribution

It introduces a comprehensive phase diagram for doped honeycomb lattices considering extended interactions, highlighting the suppression of chiral d-wave superconductivity by exchange coupling.

Findings

Identification of multiple competing phases including superconductivity and magnetic orders.

Chiral d-wave superconductivity is suppressed by weak nearest-neighbor exchange.

Presence of spin-density-wave phase near van Hove filling.

Abstract

Motivated by recent discovery of correlated insulating and superconducting behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice doped close to the van Hove singularity, using the truncated unity functional renormalization group approach. We consider an extended Hubbard model on the honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions, and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By varying the strength of the nearest-neighbor exchange coupling and Coulomb repulsion as free parameters, we present rich ground-state phase diagrams which contain the spin-triplet $f$-wave and spin-singlet chiral $d$-wave superconducting phases, the commensurate and incommensurate spin- and charge-density-wave phases, and the ferromagnetic phase. In the absence of the exchange coupling and for small value of the nearest-neighbor repulsion, the four-sublattice spin-density-wave phase is generated right around the van Hove filling, while the chiral $d$-wave superconductivity emerges slightly away from it. Surprisingly, the chiral $d$-wave superconductivity is strongly suppressed by weak nearest-neighbor exchange coupling in our calculations. We argue that this suppression might be one of the reasons why the chiral superconductivity proposed for doped graphene has not yet been observed experimentally.