Interplay of superconductivity and spin-density-wave order in doped graphene

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. 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 T c , 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 coexist. 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 coexist and are separated by first-order transitions, either as a function of doping or as a function of T .