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

TL;DR

This study uses advanced theoretical methods to analyze the electronic structure and superconducting mechanism of La$_3$Ni$_2$O$_7$, revealing key factors affecting its low superconducting transition temperature.

Contribution

It provides a detailed theoretical investigation of the pairing mechanism and the role of different subsystems in La$_3$Ni$_2$O$_7$, explaining the suppression of $T_c$.

Findings

Superconductivity primarily resides in the trilayer subsystem.

Hole doping decreases pairing strength, reducing $T_c$.

Interlayer Josephson coupling suppresses global $T_c$.

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$_7$.