Theoretical investigation of superconductivity in trilayer square-planar nickelates

The discovery of superconductivity in Sr-doped 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. NdNiO${}_2$ is the infinite-layer member of a family of square-planar nickelates with general chemical formula R${}_{n+1}$Ni${}_n$O${}_{2n+2}$ (R = La, Pr, Nd, $n= 2, 3, … \infty$). In this letter, we investigate superconductivity in the trilayer member of this series (R${}_4$Ni${}_3$O${}_8$) using a combination of first-principles and $t-J$ model calculations. R${}_4$Ni${}_3$O${}_8$ compounds resemble cuprates more than 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 R${}_4$Ni${}_3$O${}_8$ compounds is considerably stronger with a maximum gap about four times larger than that in Sr${}_{0.2}$Nd${}_{0.8}$NiO${}_2$.