[论文解读] Hund's Rule, Interorbital Hybridization, and High-$T_c$ Superconductivity in the Bilayer Nickelate

Xing-Zhou Qu, Dai-Wei Qu+3 more|arXiv (Cornell University)|Nov 21, 2023

Physics of Superconductivity and Magnetism被引用 8

一句话总结

论文在La3Ni2O7的两轨道双层t-J模型上结合DMRG和有限温度张量网络方法，发现以d_{x^{2}-y^{2}}轨道主导的跨轨道超导性具有鲁棒性，并阐明Hund点规则耦合与轨道间混杂的作用。

ABSTRACT

Understanding the pairing mechanism in bilayer nickelate superconductors constitutes a fascinating quest. Here we investigate the intriguing interplay between Hund's rule coupling and interorbital hybridization in a two-orbital model for bilayer nickelates, using a comprehensive tensor network approach: density matrix renormalization group for finite-size systems, infinite projected entangled-pair states in the thermodynamic limit, and thermal tensor networks for finite-temperature properties. We explain the pressure-dependent high-$T_c$ superconductivity observed in experiment, by identifying three distinct superconductive (SC) regimes: hybridization dominant, Hund's rule dominant, and the hybrid-Hund synergistic SC regimes. In these SC regimes, both $d_{x^2-y^2}$ and $d_{z^2}$ orbitals exhibit algebraic pairing correlations with similar Luttinger parameters $K_{\mathrm{SC}}$. However, the former exhibits a much stronger amplitude than the latter, with a distinctly higher SC characteristic temperature $T_c^*$, below which the pairing susceptibility diverges as $χ_{\mathrm{SC}}(T) \sim 1/T^{2-K_{\mathrm{SC}}}$. With realistic model parameters, we find the pressurized La$_3$Ni$_2$O$_7$ falls into the Hund's rule dominated SC regime. As hybridization further enhances with pressure, it leads to significant interorbital frustration and in turn suppresses the SC correlations, explaining the rise and fall of high-$T_c$ superconductivity under high pressure. Our results offer a comprehensive understanding of the interlayer pairing in superconducting La$_3$Ni$_2$O$_7$.

研究动机与目标

• 研究两种e_g轨道（d_{x^{2}-y^{2}}和d_{z^{2}}）在压力下如何影响La3Ni2O7的超导性。
• 确定轨道间混杂和Hund点规则耦合对超导序的影响。
• 量化基态配对相关与有限温度配对易感性在两个轨道上的表现。
• 识别在何种条件下每种机制（Hund点规则对比混杂）稳定超导性。
• 阐明两轨道在介导配对过程中的诶迁移性与局域化之间的比较角色。

提出的方法

• 研究具有intralayer t_c、J_c和ininterlayer t_perp、J_perp的双层t-J模型，分别用于d_{x^{2}-y^{2}}和d_{z^{2}}轨道。
• 包含轨道间混杂V以及具有旋转不变形式的On-site Hund点规则耦合J_H。
• 在2×L_x梯子上使用零温DMRG（最多L_x=64，最多D^*=4,500个多重态），并在L_x=24上使用有限温度切空间TRG。
• 计算轨道分辨的配对相关性 \Phi_{zz}(r) \\ 以及配对易感性SC在小配对场下以识别发散行为。
• 对模型参数进行调整以反映来自DFT的实际值（如 t_c、t_perp、t_d、V、∇…等），并探索Hund点规则与混杂主导的参数空间。

实验结果

研究问题

• RQ1 d_{x^{2}-y^{2}}与d_{z^{2}}轨道的超导相关性强度之相对比较？
• RQ2 轨道间混杂V与Hund点规则耦合J_H如何影响超导序的出现与鲁棒性？
• RQ3 Hund点规则耦合是否能将来自d_{z^{2}}的层间反铁配相关传递给d_{x^{2}-y^{2}}以促成配对？
• RQ4 是否存在由Hund点规则主导的超导相与由混杂主导的超导相，以及两者之间存在一个非超导区域？
• RQ5 从轨道分辨的配对易感性估算的高温超导尺度Tc^*是多少？

主要发现

• 基态中d_{x^{2}-y^{2}}与d_{z^{2}}轨道均显示代数级的超导配对，d_{x^{2}-y^{2}}更强。
• 有限温度下的配对易感性呈幂律发散，d_{x^{2}-y^{2}}轨道的Tc^*≈0.03 t_c，d_{z^{2}}的发散较弱。
• 充足的Hund点规则耦合(J_H ≳ 1 eV)使层间AF相关能够传递到d_{x^{2}-y^{2}}轨道，促进稳健的超导。
• 混杂作用也可以稳定超导；在强V下，即使J_H不大，超导也可能出现；但当J_H与V竞争时会出现中间的非超导区。
• 识别出两种超导区：由Hund点规则主导的超导和由混杂主导的超导，它们之间由非超导区分隔。
• d_{x^{2}-y^{2}}轨道在层内具有离子性但在两层之间具有传导性，负责高Tc超导；d_{z^{2}}轨道局域化且几乎接近半满。