Title: A Strong-Coupling-Limit Study on the Pairing Mechanism in the Pressurized La$_3$Ni$_2$O$_7$ Show Chinese title

Title: 一种在高压下La$_3$Ni$_2$O$_7$中的配对机制的强耦合极限研究

Abstract: Recently, the bilayer perovskite nickelate La$_3$Ni$_2$O$_7$ has been reported to exhibit high-temperature superconductivity (SC) near $80$K under a moderate pressure of about $14$GPa. To investigate the underlying pairing mechanism and symmetry in this complex system, we propose and analyze a mixed spin-$1$ and spin-$\frac{1}{2}$ bilayer $t$-$J$ model in the strong coupling regime. This model explicitly incorporates the crucial role of strong Hund's coupling, which favors the formation of local spin-triplet states from the two onsite $E_g$ orbital electrons at half-filling. We further investigate the model using both slave-particle mean-field theory and the density matrix renormalization group method. Our simulation results reveal that the dominate pairing channel is the interlayer one in the $3d_{x^2-y^2}$ orbital. The Hund's coupling is shown to enhance SC within a reasonable physical range. Moreover, electron doping strengthens SC by increasing carrier density; in contrast, hole doping weakens SC. These findings offer critical insights into the unconventional SC of pressurized La$_3$Ni$_2$O$_7$ and underline the important role of orbital-selective behavior and Hund's rule. Show Chinese abstract

Abstract: 最近，双层钙钛矿镍酸盐 La$_3$Ni$_2$O$_7$在约$14$GPa 的中等压力下被报道在$80$K 附近表现出高温超导性（SC）。 为了研究这个复杂系统中的配对机制和对称性，我们在强耦合 regime 中提出并分析了一个混合自旋-$1$和自旋-$\frac{1}{2}$的双层$t$-$J$模型。 该模型明确地包含了强 Hund 耦合的关键作用，这有利于在半填充时由两个局域$E_g$轨道电子形成局部自旋三重态。 我们进一步使用了 slave-particle 平均场理论和密度矩阵重整化群方法来研究该模型。 我们的模拟结果表明，在$3d_{x^2-y^2}$轨道中，主导的配对通道是层间配对。 显示 Hund 耦合在合理的物理范围内增强了 SC。 此外，电子掺杂通过增加载流子密度来增强 SC；相反，空穴掺杂则削弱 SC。 这些发现为加压 La$_3$Ni$_2$O$_7$的非常规 SC 提供了关键见解，并强调了轨道选择性行为和 Hund 规则的重要作用。