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

Motivated by the recent observation of superconductivity in strontium-doped ${\mathrm{NdNiO}}_2$, 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 degrees of accuracy. We study superconductivity in both models using the random phase approximation. 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.

Figure 1

(a) View of the crystal structure of ${\mathrm{NdNiO}}_2$. Ni, O, and Nd atoms are represented by gray, red, and orange spheres. The planar coordination in the ${\mathrm{NiO}}_2$ is highlighted by a gray square. (b) The resulting crystal field is characterized by a top $d_{x^2-y^2}$ orbital, which is singly occupied in a $d^9$ electronic configuration. (c) Crystal field acting on the formally empty Nd $d$ orbitals. In (b) and (c), the crystal-field levels are given in eV, with respect to the Ni $d_{x^2-y^2}$.

Figure 2

(a) First-principles band structure and (b) density of states of ${\mathrm{NdNiO}}_2$ with lattice parameters forced by the commensuration to the ${\mathrm{SrTiO}}_3$ substrate. The red (Ni $d_{x^2-y^2}$), yellow (Nd $d_{z^2}$), and blue (Nd $d_{xy}$) symbols emphasize the relevant orbitals that contribute to the low-energy description. In (b) the black curve refers to the sum of the individual contributions. Views of the Fermi surface of ${\mathrm{NdNiO}}_2$ at (c) pristine filling ($n=1.0$) and (d) upon 0.2 hole doping ($n=0.8$). The color scale reports the momentum dependence of the inverse Fermi velocity $[1/v_F\left(\mathbf{k}\right)]$, which is a measure of the DOS. The $\alpha$ Fermi surface displays a van Hove feature evolving from the $k_z=0$ cut to the $k_z=\pi$ cut, where it changes from a hole pocket around the $M$ point in the $k_z=0$ plane to an electron pocket around the $Z$ point in the $k_z=\pi$ plane.

Figure 3

Bare susceptibility (left panels) and pairing eigenvalues as a function of the interaction $U_{\text{Ni}}$ (right panels) for electron filling $n=1.0$ (top row) and $n=0.8$ (bottom row), respectively. Here, we adopt $U_{\text{Ni}}=U_{\text{Nd}}$ and $J_{\text{Nd}}/U_{\text{Nd}}=0.15$.

Figure 4

(a) The $d_{x^2-y^2}$-wave gap as a function doping with $J_1=J_2=0.1$ eV. Positive (negative) values relate to electron (hole) doping. (b) Superconducting gap for $d_{x^2-y^2}$-wave pairing. In the calculations, a $k$ mesh of $100\times 100\times 50$ has been adopted.