标题： 磁致介导的加压三元镍氧化物 La$_4$Ni$_3$O$_{10}$中的跨层配对 显示英文标题

标题： Magnetically Mediated Cross-Layer Pairing in Pressurized Trilayer Nickelate La$_4$Ni$_3$O$_{10}$

摘要： 最近发现的三层镍酸盐超导体 La$_4$Ni$_3$O$_{10}$在压力下已成为探索非常规超导性的有前途的平台。然而，配对机制仍然是活跃研究的主题。通过在现实的两轨道三层 Hubbard 模型上的大规模密度矩阵重整化群计算，我们阐明了该系统中的超导（SC）机制。我们的结果揭示了两种不同轨道中的显著磁性关联：虽然$d_{z^2}$轨道表现出层间和跨层反铁磁（AFM）关联，而$d_{x^2-y^2}$轨道仅表现出跨层 AFM 关联，使得后者具有准长程 SC 顺序。我们证明了 Hund 规则耦合对于形成 SC 顺序是必不可少的，并讨论了动能 AFM 关联和 Hubbard 排斥$U$的影响。 我们的发现促使进一步简化三层Hubbard模型为有效的双层混合维度$t$-$J$模型，为理解三层和双层镍氧化物中的层间SC提供了一个统一的框架。 显示英文摘要

摘要： The recently discovered trilayer nickelate superconductor La$_4$Ni$_3$O$_{10}$ under pressure has emerged as a promising platform for exploring unconventional superconductivity. However, the pairing mechanism remains a subject of active investigations. With large-scale density matrix renormalization group calculations on a realistic two-orbital trilayer Hubbard model, we elucidate the superconducting (SC) mechanism in this system. Our results reveal distinct magnetic correlations in the two different orbitals: while the $d_{z^2}$ orbital exhibits both interlayer and cross-layer antiferromagnetic (AFM) correlations, the $d_{x^2-y^2}$ orbital shows exclusively cross-layer AFM correlations, rendering a quasi-long-range SC order in the latter. We demonstrate that the Hund's rule coupling is essential for forming the SC order, and discuss the effects of kinetic AFM correlation and Hubbard repulsive $U$. Our findings motivate a further simplification of the trilayer Hubbard to an effective bilayer mixed-dimensional $t$-$J$ model, providing a unified framework for understanding interlayer SC in both trilayer and bilayer nickelates.