Pairing mechanism and superconductivity in pressurized La$_5$Ni$_3$O$_{11}$</inline-formula>

The discovery of superconductivity (SC) with critical temperature $T_c$ above the boiling point of liquid nitrogen in pressurized La$_3$Ni$_2$O$_{7}$ has sparked a surge of exploration of high-$T_c$ superconductors in the Ruddlesden-Popper (RP) phase nickelates. More recently, the RP phase nickelate La$_5$Ni$_3$O$_{11}$, which hosts a layered structure with alternating bilayer and single-layer NiO$_2$ planes, has been reported to accommodate SC under pressure, exhibiting a dome-shaped pressure dependence with the highest $T_c\approx~64$ K, capturing a lot of interest. Here, using density functional theory (DFT) and random phase approximation (RPA) calculations, we systematically study the electronic properties and superconducting mechanism of this material. Our DFT calculations yield a band structure including two nearly decoupled sets of sub-band structures, with one set originating from the bilayer subsystem and the other from the single-layer one. RPA-based analysis demonstrates that SC in this material occurs primarily within the bilayer subsystem exhibiting an $s^\pm$ wave pairing symmetry similar to that observed in pressurized La$_3$Ni$_2$O$_{7}$, while the single-layer subsystem mainly serves as a bridge facilitating the inter-bilayer phase coherence through the interlayer Josephson coupling (IJC). Since the IJC thus attained is extremely weak, it experiences a prominent enhancement under pressure, leading to the increase of the bulk $T_c$ with pressure initially. When the pressure is high enough, the $T_c$ gradually decreases due to the reduced density of states on the $\gamma$-pocket. In this way, the dome-shaped pressure dependence of $T_c$ observed experimentally is naturally understood.

在加压La₃Ni₂O₇中发现临界温度T_c高于液氮沸点的超导（superconductivity，SC）现象，引发了Ruddlesden-Popper（RP）相镍酸盐基高温超导体的研究热潮。近期，具有交替双层与单层NiO₂平面层状结构的RP相镍酸盐La₅Ni₃O₁₁被报道在加压条件下具备超导性，其T_c呈现穹顶状的压力依赖性，最高T_c约为64开尔文，引发了广泛关注。本文基于密度泛函理论（density functional theory，DFT）与随机相位近似（random phase approximation，RPA）计算，系统研究了该材料的电子性质与超导机制。DFT计算得到的能带结构包含两组近乎解耦的子能带：一组源于双层子系统，另一组来自单层子系统。基于RPA的分析表明，该材料中的超导主要发生在双层子系统中，其配对对称性为s±波，与加压La₃Ni₂O₇中观测到的配对对称性类似；而单层子系统主要充当桥梁，通过层间约瑟夫森耦合（interlayer Josephson coupling，IJC）促进双层间的相位相干。由于所获得的层间约瑟夫森耦合极弱，其在加压条件下会显著增强，进而使体相T_c随压力升高在初始阶段上升。当压力足够高时，由于γ口袋处的态密度降低，T_c会逐渐下降。这一机制自然解释了实验中观测到的T_c随压力变化的穹顶状规律。