Superconducting two-dimensional materials, and in particular few‐layer graphene, offer an exciting platform for low‐power electronics, yet the origin of their unconventional superconductivity remains an open question. Prevailing theories, primarily rooted in the Bardeen-Cooper-Schrieffer (BCS) framework that assumes electron-phonon interactions are the main mechanism of superconductivity, struggle to account quantitatively for the observed phenomena. Recent studies point to a plasmonic pairing mechanism in graphene systems; however, disentangling the relative contributions of phonon- and plasmon-mediated pairing remains challenging due to the lack of a satisfactory first-principles framework capable of accurately capturing dynamical screening effects in the electronic channel. Here, we present a theoretical framework that extends the quasiparticle self-consistent GW method to the superconducting phase by coupling it with the Eliashberg treatment of both phonon- and plasmon-mediated interactions. Our approach, termed superconducting quasiparticle GW (s-qpGW), is on par with the state-of-the-art Eliashberg theory of superconductivity when applied to bulk metals, and correctly predicts the absence of superconductivity in doped monolayer graphene. To differentiate s-qpGW from conventional Eliashberg approaches, we study a simple model system, graphene with an artificially enhanced density of states, and demonstrate that s-qpGW captures dynamical Coulomb screening effects in ways that standard BCS theory cannot.

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• Superconductivity
• 2-dimensional systems
• Graphene
• Unconventional superconductors
• Eliashberg theory
• GW method
• Methods in superconductivity