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The discovery of superconductivity in Ruddlesden–Popper (RP) phase layered nickelates under high pressure has opened a new avenue for exploring unconventional pairing mechanisms beyond cuprates and iron-based superconductors. In particular, La3Ni2O7 exhibits a superconducting transition temperature ($ T_c $) as high as 80 K at ~15 GPa, making it the second class of oxides that achieve liquid-nitrogen-temperature superconductivity. Subsequent experiments have extended superconductivity to related compounds such as La4Ni3O10 and La5Ni3O11, as well as epitaxially grown thin films at ambient pressure. These findings have motivated extensive theoretical efforts to elucidate the microscopic pairing mechanism. This review summarizes recent progress from the perspective of weak-coupling theories, including random phase approximation (RPA), functional renormalization group (FRG), and fluctuation-exchange (FLEX) approaches. Density functional theory (DFT) calculations reveal that the low-energy degrees of freedom are dominated by Ni 3$ d_{z^2} $ and 3$ d_{x^2-y^2} $ orbitals. In La3Ni2O7, pressure-induced metallization of the bonding 3$ d_{z^2} $ band produces the γ pocket, enhancing spin fluctuations and stabilizing superconductivity. These fluctuations support superconductivity through interlayer 3$ d_{z^2} $ pairing characterized by an $ s^{\pm} $ gap. Hole doping or substitution may restore the γ pocket and enable bulk superconductivity at ambient pressure. For La4Ni3O10, theoretical calculations indicate predominantly $ s^{\pm} $ pairing from interlayer 3$ d_{z^2} $ orbitals, with weaker strength than La3Ni2O7, explaining its lower $ T_c $ and showing little sensitivity to band structure. In La5Ni3O11, composed of alternating single-layer and bilayer units, superconductivity mainly arises from the bilayer subsystem, again dominated by 3$ d_{z^2} $ orbitals. Interestingly, the interplay between inter-bilayer Josephson coupling and the suppression of density of states leads to a dome-shaped $ T_c $–pressure phase diagram, distinct from the monotonic behavior of La3Ni2O7. Epitaxial (La, Pr)3Ni2O7 thin films display superconductivity above 40 K at ambient pressure. Theory predicts doping-dependent pairing: $ s^{\pm} $ symmetry is favored at low doping levels, while dxy pairing emerges at higher doping, in agreement with experimental indications of both nodeless and nodal gap behaviors. Beyond superconductivity, experiments have revealed spin-density-wave (SDW) order in bulk La3Ni2O7 and La4Ni3O10 at ambient pressure. Weak-coupling calculations confirm that these SDWs are driven by Fermi surface nesting and that their suppression under pressure gives rise to strong spin fluctuations which act as the glue for Cooper pairing. This highlights the intimate connection between the density-wave parent states and high-pressure superconductivity in nickelates. In summary, weak-coupling theories provide a unified framework for RP nickelates, highlighting the key role of 3$ d_{z^2} $ orbitals, interlayer pairing, and spin fluctuations. They suggest that pressure, doping, substitution, and epitaxial strain can optimize superconductivity and potentially achieve high-$ T_c $ phases at ambient pressure. Key challenges remain in clarifying orbital competition, the SDW-superconductivity interplay, and strong-correlation effects, requiring close collaboration between advanced experiments and multi-orbital many-body theory. -
Keywords:
- unconventional superconductivity /
- pairing symmetry /
- nickelate superconductors /
- weak-coupling theory
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图 3 La3Ni2O7的全压力-温度相图, 压力范围从常压到100 GPa[35]
图 6 La3Ni2O7的电子结构特征 (a) 高压(29.5 GPa) 下的能带结构及各轨道成分的态密度[1] (b) 对应图(a)的费米口袋[49], 颜色表示轨道成分 (c) 低压(1.6 GPa)下的能带结构及各轨道成分的态密度[1] (d) 与图(c)对应的费米口袋[18]. (a, c)中黑色箭头指向$ d_{z^2} $轨道成键态能带 (e) 常压下$ d_{z^2} $轨道成键态能带(即γ)位于费米能级以下的ARPES实验证据[18] (f) Ni-$ d_{x^2-y^2} $轨道和Ni-$ d_{z^2} $轨道通过与O-$ p_{x, y} $轨道和O-$ p_{z} $轨道杂化成键[1] (g) 原胞内二个Ni原子的3d电子能级结构与占据情况[1]
图 8 SrLaAlO4衬底上的(La, Pr)3Ni2O7薄膜的ARPES实验结果. 对于Ni-$ 3 d_{z^2} $成键能带是否穿过费米能而形成γ口袋, 不同实验给出了不同的结果 (a) 文献[62]报告的ARPES测得的费米面形状, 深色部分对应费米面[62] (b) 文献[62]中分析ARPES结果得到的费米面[62] (c) 文献[20]中报告的沿高对称线的能带结构. 图中标记了β和γ能带的位置, 其中γ能带的顶部位于蓝色区域, 该结果显示γ能带完全位于费米能量以下而没有穿过费米能[20]. 小图为大图的虚线框区域的放大 (d) 文献[20]中分析ARPES结果得到的费米面[20]
图 9 高压下La3Ni2O7的RPA计算结果[68] (a) $ \chi^{(s)} $的最大本征值在布里渊区的分布, 最强自旋涨落的波矢记为$ Q_{1} $, 其余较强的自旋涨落波矢记为$ Q_{2} $、$ Q_{3} $ (b) 不同配对对称性的配对本征值λ随U变化的函数关系 (c) $ s^{\pm} $配对的能隙函数在费米面上的分布, $ Q_1 $为费米口袋的嵌套矢量, 与图(a)中的自旋涨落矢量相等
图 12 高压La3Ni2O7中顶角氧缺陷对超导的影响的RPA研究[68] (a) 相互作用强度U-顶角氧缺陷浓度δ相图. SC和LMP分别表示超导和局域磁序, 黑色实线表示临界相互作用$ U_c $ (b) 磁矩在实空间的分布, 颜色表示磁矩大小. 红色虚线框内为顶角氧缺陷位置 (c) 超导$ T_c $与顶角氧缺陷浓度δ的关系
图 13 RPA计算得到的La4Ni3O10的自旋极化率以及超导[57] (a) RPA重整化自旋极化率在第一布里渊区的分布, 其最大值位于$ {\bf{Q}}_1 $ (b) 各配对对称性的配对本征值λ的最大值对U的依赖 (c) 体系中主导的配对能隙$ s^{\pm} $波在费米面的分布, 其中$ {\bf{Q}}_1 $矢量联系了$ \alpha_1 $口袋和γ口袋之间的费米面嵌套 (d) 各配对对称性的配对本征值λ的最大值对掺杂浓度δ的依赖
图 15 La5Ni3O11中超导对压力的依赖[58] (a) 体系态密度(DOS, 红线)和RPA计算得到的超导配对本征值λ(黑线)对压力的依赖 (b) La5Ni3O11中超导态-正常态-超导态的约瑟夫森结构示意图 (c) La5Ni3O11中超导$ T_c $的压力依赖
图 16 (La, Pr)3Ni2O7/SrLaALO4薄膜的RPA计算结果[63] (a) 超导配对对称性与空穴掺杂程度δ的关系 (b—d) 空穴掺杂程度$ \delta=0.1 $情形 (b) 自旋极化率的最大本征值在布里渊区的分布, $ \boldsymbol{Q}_1 $为最大值所在位置 (c) 不同配对对称性的配对本征值λ随U的变化. 在所有U下均有s波的λ最大, 体系最终实现的超导配对为s波 (d) 费米面上的能隙函数分布. $ \boldsymbol{Q}_1 $为费米面嵌套矢量 (e—g) 空穴掺杂程度$ \delta=0.23 $情形 (e) 自旋极化率的最大本征值在布里渊区的分布, $ \boldsymbol{Q}_2 $为最大值所在位置 (f) 不同配对对称性的配对本征值λ随U的变化. 在所有U下均有$ d_{xy} $波的λ最大, 体系最终实现的超导配对为$ d_{xy} $波 (g) 费米面上的能隙函数分布. $ \boldsymbol{Q}_2 $为费米面嵌套矢量
图 18 常压下La3Ni2O7的RPA计算结果[71] (a) 常压下La3Ni2O7在折叠布里渊区中的能带结构. TB能带(红线)与DFT能带(黑线)在低能附近基本一致 (b) 与图(a)能带对应的费米口袋. Q为费米口袋嵌套矢量 (c) 自旋极化率$ \chi^{(s)} $的最大本征值在布里渊区的分布, 其最大值位置对应图(b)中的费米口袋嵌套矢量Q (d) 磁矩在实空间的面内分布. 元胞(虚线椭圆)包含A, B子格, $ e_{x/y} $与$ e_{a/b} $为两套格矢, 分布对应折叠和扩展的布里渊区
图 19 常压下La4Ni3O10的RPA计算结果[78] (a) 常压下La4Ni3O10在第一布里渊区的费米面, $ {\bf{Q}} $矢量联系了其中的费米面嵌套 (b) 实空间中的SDW模式 (c) 当$ V=0 $时, $ \chi^s $随$ J_H $的变化情况, 其中亮点代表自旋密度波波矢所在位置 (d) λ的最大值对掺杂浓度δ的依赖, 其中$ J_H=U/6 $
表 1 RP相镍基超导弱耦合理论研究汇总对比表
Table 1. Summary and Comparison Table of Weak Coupling Theory Research on RP-Phase NickelateSuperconductors
材料体系 计算方法 模型关键特征 主要结论摘要 La3Ni2O7
(块材, 高压)RPA [68] 双层两轨道($ d_{x^2-y^2}, d_{z^2} $) 最强自旋涨落波矢$ Q\approx(\pi, 0) $. $ s^{\pm} $波配对, 能隙在$ \gamma/\alpha $口袋与β口袋上符号相反. 超导由层间$ d_{z^2} $轨道配对主导. FRG [69] 双层两轨道($ d_{x^2-y^2}, d_{z^2} $) 与RPA [63]定性一致 FLEX [70] 双层两轨道($ d_{x^2-y^2}, d_{z^2} $) 与RPA/FRG结论一致. 发现解除$ d_{x^2-y^2} $与$ d_{z^2} $轨道间的杂化能显著增强$ T_c $. La4Ni3O10
(块材, 高压)RPA [57] 三层多轨道模型 最强自旋涨落波矢$ Q\approx(\pi, \pi) $. $ s^{\pm} $波配对, 对能带细节不敏感. 超导由外层$ d_{{z^2}^2} $轨道间层间配对主导. FRG [56] 三层多轨道模型(考虑$ \alpha_1 $口袋缺失) 与RPA定性一致, 支持$ s^{\pm} $波配对. 强调洪特耦合对超导的影响. 费米面嵌套和能隙分布细节与RPA略有不同. FLEX [54] 三层多轨道模型 解释其相对较低的$ T_c $. La5Ni3O11
(块材, 高压)RPA [58] 解耦近似(单层+双层子系统) 超导主要发生在双层子系统内, 为$ s^{\pm} $波配对. 穹顶型$ T_c $-P相图与层间约瑟夫森耦合有关. (La, Pr)3Ni2O7
(薄膜, 常压)RPA [63] 存在γ口袋的假说 配对对称性随空穴掺杂δ变化
在实验关注的$ \delta\sim0.21 $附近, 为$ d_{xy} $波.DMFT+RPA [42] 动力学平均场重整化能带 得到$ s^{\pm} $波配对. FRG [77] 费米口袋形状近正方形 不同口袋间嵌套支持$ s^{\pm} $波配对. 
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