Kekul\'e superconductivity and antiferromagnetism on the graphene lattice

TL;DR

This study uses the variational cluster approximation to analyze superconductivity in the graphene lattice, revealing that Kekulé $p+ip$-wave pairing is most favored and can coexist with antiferromagnetism, enhancing both orders.

Contribution

It demonstrates that Kekulé $p+ip$-wave superconductivity is the dominant pairing symmetry on the graphene lattice and can coexist with antiferromagnetism, extending previous findings.

Findings

Kekulé $p+ip$-wave pairing is most favored in the phase diagram.

Antiferromagnetism can coexist and be enhanced with Kekulé superconductivity.

The coexistence of orders suggests intertwined phases in the model.

Abstract

We investigate superconducting order in the extended Hubbard model on the two-dimensional graphene lattice using the variational cluster approximation (VCA) with an exact diagonalization solver at zero temperature. Building on the results of Ref.$[1]$, which identified triplet $p$- and $p+ip$-wave superconductivity as the most favored pairing symmetries in that model, we place uniform SC solutions in competition with the proposed nonuniform Kekul\'e ($p+ip$-K) superconducting pattern proposed in Ref.$[2]$. We find that the $p+ip$-K solution is in fact the most favored pairing in most of the phase diagram. In addition, we show that antiferromagnetism can co-exist with the $p+ip$-K state and that both orders are enhanced by their coexistence.