Quasiparticle GW for Superconductors: Toward a Unified Treatment of Electron-Phonon and Electron-Plasmon Couplings

Abstract

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 new 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 "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.