Interplay of superconductivity and spin density wave order in doped graphene

TL;DR

This paper investigates the competition between superconductivity and spin density wave order in doped graphene at Van Hove doping, revealing they do not coexist but are separated by first-order transitions.

Contribution

It provides a theoretical analysis of the interplay between superconductivity and spin density wave order in doped graphene, deriving a Landau-Ginzburg functional to describe their interactions.

Findings

Superconductivity is strongest at Van Hove doping with highest Tc.

Spin density wave likely emerges slightly away from Van Hove doping.

Superconductivity and spin density wave do not coexist, separated by first-order transitions.

Abstract

We study the interplay between superconductivity and spin density wave order in graphene doped to 3/8 or 5/8 filling (a Van Hove doping). At this doping level, the system is known to exhibit weak coupling instabilities to both chiral d + id superconductivity and to a uniaxial spin density wave. Right at van Hove doping, the superconducting instability is strongest and emerges at the highest Tc, but slightly away from van-Hove doping a spin-density-wave likely emerges first. We investigate whether at some lower temperature superconductivity and spin-density-waves co-exist. We derive the Landau-Ginzburg functional describing interplay of the two order parameters. Our calculations show that superconductivity and spin density wave order do not co-exist and are separated by first-order transitions, either as a function of doping or as a function of T.