Pairing mechanism and superconductivity in 1313 phase La${}_3$Ni${}_2$O${}_7$

Abstract

Recently, the observation of superconductivity (SC) with $T_c$ $\approx$ 3.6 K in the pressurized 1313 La${}_3$Ni${}_2$O${}_7$ has attracted considerable interest. Here, we systematically investigate the electronic properties and superconducting mechanism of 1313 La${}_3$Ni${}_2$O${}_7$ using density functional theory plus dynamical mean-field theory (DFT+DMFT) and random phase approximation (RPA). Our DFT+DMFT calculations reveal that the single-layer (SL) subsystem exhibits nearly insulating behavior, with the $d_{z^2}$ orbital showing Mott physics, while the trilayer (TL) subsystem remains metallic. This indicates that SC primarily resides in the TL subsystem, whose Ni-$e_g$ orbitals are found to be hole-doped relative to bulk La${}_4$Ni${}_3$O${}_{10}$. Based on DFT+DMFT-derived low-energy Hamiltonian, RPA-based analysis yields an $s^{\pm }$-wave pairing symmetry within the TL subsystem. Importantly, we identify two key factors that contribute to the significant suppression of $T_c$ in 1313 La${}_3$Ni${}_2$O${}_7$ compared to bulk La${}_4$Ni${}_3$O${}_{10}$. First, the hole doping in the TL subsystem, as established by DMFT, leads to a decreased pairing strength, as confirmed by RPA calculations -- a trend resembling that in bulk La${}_4$Ni${}_3$O${}_{10}$. Second, the SL subsystem acts as a bridge connecting adjacent superconducting TL subsystems, thereby forming an S-N-S Josephson junction. The resulting interlayer Josephson coupling governs the phase coherence between TL subsystems and further suppresses the global $T_c$. Combinedly, our findings suggest that the high-$T_c$ phase in the RP La${}_3$Ni${}_2$O${}_7$ family should be attributed to the 2222 La${}_3$Ni${}_2$O${}_7$ rather than the 1313 La${}_3$Ni${}_2$O${}_7$.

6 pages, 5 figures

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