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Electronic structures and superconductivity in Nd-doped La$_3$Ni$_2$O$_7$

The recent discovery of high-$T_c$ superconductivity in Ruddlesden-Popper (RP) nickelates has motivated extensive efforts to explore higher $T_c$ superconductors. Here, we systematically investigate Nd-doped La$_3$Ni$_2$O$_7$ using density functional theory (DFT) and renormalized mean-field theory (RMFT). DFT calculations reveal that both the lattice constants and interlayer spacing decrease upon Nd substitution, similar to the effect of physical pressure. However, the in-plane Ni-O-Ni bond angle evolves non-monotonically with doping, increasing to a maximum at 70% ($\sim$ 2/3) Nd doping level and then falling sharply at 80%, which leads to a reduction in orbital overlap. Moreover, Nd doping has a more pronounced effect on the Ni-$d{_{z^2}}$ orbital, demonstrating an orbital-dependent effect of rare-earth substitution. Through the bilayer two-orbital $t-J$ model, RMFT analysis further shows an $s\pm$-wave pairing symmetry, with $T_c$ rising to a maximum at about 70% Nd substitution before declining, in agreement with the transport measurements. The variation in $T_c$ can be traced to the competition between continuously enhanced interlayer superexchange coupling $J_\perp^z$ and a gradual decrease in particle density. These results highlight the delicate interplay among structural tuning, orbital hybridization, and superconductivity, providing important clues to design higher-$T_c$ RP nickelate superconductors.