Robust $d_{x^2-y^2}$-wave superconductivity of infinite-layer nickelates

Motivated by the recent observation of superconductivity in strontium doped NdNiO$_2$, we study the superconducting instabilities in this system from various vantage points. Starting with first-principles calculations, we construct two distinct tight-binding models, a simpler single-orbital as well as a three-orbital model, both of which capture the key low energy degrees of freedom to varying degree of accuracy. We study superconductivity in both models using the random phase approximation (RPA). We then analyze the problem at stronger coupling, and study the dominant pairing instability in the associated t-J model limit. In all instances, the dominant pairing tendency is in the $d_{x^2-y^2}$ channel, analogous to the cuprate superconductors.