Theoretical investigation of superconductivity in trilayer square-planar nickelates

Abstract

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, $n=2,3,...\ensuremath{\infty}$). 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 $t\ensuremath{-}J$ model calculations. ${\mathrm{R}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{8}$ compounds resemble cuprates more than ${\mathrm{RNiO}}_{2}$ materials in that only Ni-${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ 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 ${\mathrm{Sr}}_{0.2}{\mathrm{Nd}}_{0.8}{\mathrm{NiO}}_{2}$.