This paper introduces s-qpGW, a new computational framework that extends the quasiparticle self-consistent GW (qpGW) method into the superconducting state. The authors couple qpGW to the Eliashberg theory of superconductivity so that both phonon-mediated pairing (from atomic vibrations) and plasmon-mediated pairing (from collective electronic oscillations) are treated on the same footing. The main claim is that this unified approach can capture dynamical screening effects in the electronic channel that simpler theories miss.

At a high level the method separates the screened interaction W into two parts: Wph from phonons and WC from purely electronic Coulomb screening. Electronic screening is computed in the random phase approximation (RPA) and plugged into the Eliashberg equations. The paper describes several modes of treating the Coulomb term: a fully frequency‑dependent, self-consistent s-GW treatment; a static approximation used in standard Eliashberg work that excludes plasmon effects; and common semi-empirical shortcuts based on a dimensionless parameter µ* (with typical values 0.1–0.2 and an electronic cutoff often ≈1 eV).

The authors benchmarked their approach on a few cases. For bulk metals they report that s-qpGW performs on par with state-of-the-art Eliashberg calculations. For doped monolayer graphene their method correctly predicts the absence of superconductivity. To show where s-qpGW differs from conventional approaches, they also study a simple model of graphene with an artificially enhanced density of electronic states and find that s-qpGW captures dynamical Coulomb screening and plasmonic effects that standard Bardeen-Cooper-Schrieffer (BCS) theory cannot.

This work matters because two-dimensional materials like graphene can host low-energy (acoustic) plasmons that compete with or assist phonons in forming Cooper pairs. Having a first-principles tool that treats both channels consistently helps researchers separate the roles of phonons and plasmons. That in turn can guide more reliable predictions of when superconductivity will appear in tunable 2D systems and can inform materials design for low-power electronics.