Theoretical investigation of superconductivity in trilayer square-planar nickelates

Abstract: 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$_2$.