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Recently, high temperature ($T_c\approx 80$K) superconductivity (SC) has beendiscovered in La$_3$Ni$_2$O$_7$ (LNO) under pressure. Question arises whetherthe transition temperature $T_c$ could be further enhanced under suitableconditions. A possible route for realizing higher $T_c$ is elementsubstitution. Similar SC could appear in rare-earth (RE) R$_3$Ni$_2$O$_7$ (RNO,R=RE element) material series under pressure. The electronic properties in theRNO materials are dominated by the Ni $3d$ orbitals in the bilayer NiO$_2$plane. In the strong coupling limit, the SC could be fully characterized by abilayer single $3d_{x^2-y^2}$-orbital $t$-$J_{\parallel}$-$J_{\perp}$ model.Under RE element substitution from La to RE element, the lattice constantdecreases and the electronic hopping increases, leading to strongersuperexchanges between the $3d_{x^2-y^2}$ orbitals. Based on the slave-bosonmean-field theory, we explore the pairing nature and the evolution of $T_c$ inRNO materials. Consequently, it is found that the element substitution does notalter the pairing nature, i.e. the inter-layer $s$-wave pairing is alwaysfavored in RNO. However, the $T_c$ increases from La to Sm and a nearly doubled$T_c$ is achieved for SmNO. This work provides evidence for possible higher$T_c$ R$_3$Ni$_2$O$_7$ materials, which may be realized in further experiments.

Effect of Rare-earth Element Substitution in Superconducting R$_3$Ni$_2$O$_7$ Under Pressure