Two-gap superconductivity and decisive role of rare-earth $d$ electrons in infinite-layer nickelates

Abstract

We present a theoretical prediction of a phonon-mediated two-gap superconductivity in infinite-layer nickelates Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ by performing $\textit{ab initio}$ $GW$ and $GW$ perturbation theory calculations. Electron $GW$ self-energy effects significantly alter the characters of the two-band Fermi surface and enhance the electron-phonon coupling, compared with results based on density functional theory. Solutions of the fully $\textbf{k}$-dependent anisotropic Eliashberg equations yield two dominant $s$-wave superconducting gaps - a large gap on a band of rare-earth Nd $d$ and interstitial orbital characters and a small gap on a band of transition-metal Ni $d$ character. Increasing hole doping induces a non-rigid-band response in the electronic structure, leading to a rapid drop of the superconducting $T_c$ in the overdoped regime in agreement with experiments.