The discovery of superconductivity in Sr-doped ${\mathrm{NdNiO}}_2$ is a crucial breakthrough in the long pursuit for nickel oxide materials with electronic and magnetic properties similar to those of the cuprates. ${\mathrm{NdNiO}}_2$ is the infinite-layer member of a family of square-planar nickelates with general chemical formula ${\mathrm{R}}_{n+1}{\mathrm{Ni}}_n{\mathrm{O}}_{2n+2}$ (R = La, Pr, Nd, $n=2,3,...\infty$). In this Rapid Communication, we investigate superconductivity in the trilayer member of this series (${\mathrm{R}}_4{\mathrm{Ni}}_3{\mathrm{O}}_8$) using a combination of first-principles and $t-J$ model calculations. ${\mathrm{R}}_4{\mathrm{Ni}}_3{\mathrm{O}}_8$ compounds resemble cuprates more than ${\mathrm{RNiO}}_2$ materials in that only Ni-$d_{x^2-y^2}$ bands cross the Fermi level, they exhibit a largely reduced charge transfer energy, and as a consequence superexchange interactions are significantly enhanced. We find that the superconducting instability in doped ${\mathrm{R}}_4{\mathrm{Ni}}_3{\mathrm{O}}_8$ compounds is considerably stronger with a maximum gap about four times larger than that in ${\mathrm{Sr}}_{0.2}{\mathrm{Nd}}_{0.8}{\mathrm{NiO}}_2$.

• Received 24 March 2020
• Accepted 6 July 2020

DOI:https://doi.org/10.1103/PhysRevB.102.020504