Spin fluctuations are widely believed to mediate electron pairing in unconventional superconductors. In gap-equation calculations, the random phase approximation (RPA) has been widely used to construct the spin-fluctuation pairing potential that arises from Hubbard-like interactions. However, RPA is formally valid only in the weak-coupling regime and tends to predict spin-density-wave (SDW) instabilities at unrealistically small interaction strengths. In this work, we extend RPA to intermediate and strong coupling by combining it with dynamical mean-field theory (DMFT), forming an approach we term RPA+DMFT. Within this framework, the bare susceptibility in RPA is replaced by a “dressed” susceptibility that incorporates quasiparticle dispersion and spectral weight obtained from DMFT. This dressed susceptibility is then used to construct the pairing interaction for the gap equation. We apply the RPA+DMFT method to infinite-layer nickelates and find that the leading superconducting eigenvalue exhibits a non-monotonic dependence on interaction strength, peaking at intermediate coupling, in qualitative agreement with previous studies. Furthermore, we find that the orbital hybridization in infinite-layer nickelates leads to van Hove singularities (VHS) that are pinned to the Fermi surface. Those VHS brings the system closer to magnetic instability, amplifying antiferromagnetic spin fluctuations. This naturally explains why infinite-layer nickelates such as La_0.8Sr_0.2NiO₂ exhibits a sizable superconducting transition temperature, despite the fact that the “self-doping” effect makes its Ni-d_x2−y2 orbital overdoped relative to the phase diagram of cuprates.

Reference: Chengliang Xia, Shengjie Zhou, Hanghui Chen, “Three-dimensional fermi surface, van hove singularity and enhancement of superconductivity in infinite-layer nickelates”, arXiv:2504.18778.