Recent advances and prospects in theoretical study of bilayer nickelate superconductor La3Ni2O7

ZHENG Yaoyuan; MO Shicong; WU Wei

doi:10.7498/aps.74.20250711

Abstract

The high-temperature superconductivity in bilayer nickelate La₃Ni₂O₇ under high pressures, which was discovered in 2023, has spurred intensive theoretical and numerical investigations. These studies aim to unravel physical properties of La₃Ni₂O₇ from various aspects, with particular emphasis on its pairing symmetry and underlying superconducting mechanism. Moreover, significant effort has also been made to explore and predict novel nickel-based superconductors related to La₃Ni₂O₇. This article reviews these recent advancements aimed at elucidating the physical properties and superconducting mechanism of La₃Ni₂O₇, whose multi-orbital characteristics and intricate electronic correlations have spawned diverse theories for its pairing mechanism. In this article, the recent findings on La₃Ni₂O₇ are summarized regarding its macroscopic models, pairing symmetry, normal state characteristics, and the structure of spin and charge density waves. Particular attention is paid to the debate surrounding the role of σ-bonding band metallization in superconductivity. Finally, this article also presents an outlook on future studies crucial for advancing our understanding of La₃Ni₂O₇ superconductivity.

Keywords:

Authors and contacts

School of Physics, Sun Yat-sen University, Guangzhou 510275, China

Corresponding author: WU Wei, wuwei69@mail.sysu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12494594) and the Guangdong Provincial Strategic Research Program in Quantum Science, China (Grant No. GDZX2401010).

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图 1 (a)铜氧化物YBa₂Cu₃O_7–x (YBCO)超导体的晶体结构; (b)镍氧化物La₃Ni₂O₇超导体的晶体结构; (c) La₃Ni₂O₇超导体压力下的超导相图^[29]

Figure 1. (a) Crystal structure of the copper oxide superconductor YBa₂Cu₃O_7–x (YBCO); (b) crystal structure of the nickel oxide superconductor La₃Ni₂O₇; (c) superconducting phase diagram of La₃Ni₂O₇ under pressure^[29].

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图 2 La₃Ni₂O₇的电子轨道结构与能带　(a) La₃Ni₂O₇的双层NiO₂面结构示意图, 红色图形代表$3{\mathrm{d}}_{z^2} $轨道, 蓝色图形代表$3{\mathrm{d}}_{x^2- y^2} $轨道, 在此图中几个重要的电子跃迁被标识出来, V代表面内$3{\mathrm{d}}_{x^2- y^2} $轨道和$3{\mathrm{d}}_{z^2} $轨道的杂化, t_⊥代表$3{\mathrm{d}}_{z^2} $电子之间的层间跃迁, $ {t}_{x}^{1} $是$3{\mathrm{d}}_{x^2- y^2} $电子面内最近邻跃迁, $ {t}_{z}^{1} $是$3{\mathrm{d}}_{z^2} $电子面内最近邻跃迁; (b) DFT计算得到的高压下的低能能带结构和(c) 高压下的费米面^[75], 红色代表来自$3{\mathrm{d}}_{x^2- y^2} $轨道对能带的贡献, 而蓝色代表$3{\mathrm{d}}_{z^2} $轨道的贡献; 结果显示, 在高压下γ能带出现在费米面上, 即σ成键能带金属化

Figure 2. Electronic orbital structure and dispersion relation of La₃Ni₂O₇: (a) Schematic of the NiO₂ bilayer structure of La₃Ni₂O₇, the red and blue shapes denote the $3{\mathrm{d}}_{z^2} $ and $3{\mathrm{d}}_{x^2- y^2} $ orbitals, respectively, several key electron hopping terms are labeled: V denotes hybridization between the in-plane $3{\mathrm{d}}_{x^2- y^2} $ and $3{\mathrm{d}}_{z^2} $ orbitals, t_⊥ represents the interlayer hopping of $3{\mathrm{d}}_{z^2} $ electrons, $ {t}_{x}^{1} $ is the in-plane nearest-neighbor hopping of $3{\mathrm{d}}_{x^2- y^2} $ electrons, and $ {t}_{z}^{1} $ is the in-plane nearest-neighbor hopping of $3{\mathrm{d}}_{z^2} $ electrons; (b) low-energy band structure of La₃Ni₂O₇ under high pressure (>14 GPa) obtained from DFT calculations; (c) Fermi surface under high pressure^[75]; In panels (b), (c), warm colors indicate the contribution of the $3{\mathrm{d}}_{x^2- y^2} $ orbitals to the energy bands, while cool colors represent the contribution of the $3{\mathrm{d}}_{z^2} $ orbitals. Results shown here demonstrate that under high pressure, the γ band crosses Fermi level, indicating the metallization of the σ-bonding band.

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图 3 Mott-Hubbard 绝缘体和charge-transfer绝缘体示意图　(a) 大U极限下的Mott-Hubbard绝缘体; (b) 大U极限下的charge-transfer 绝缘体; (c) 在实际材料中考虑掺杂形成d-p关联电子态的电荷转移型关联电子能态, 在费米面附近, Zhang-Rice单态能带出现, 其中UHB代表上哈伯德带, LHB代表下哈伯德带, CTB代表电荷转移带, ZRSB代表Zhang-Rice单态能带, E_F代表费米能级, Δ表示电荷转移能隙

Figure 3. Schematic plots depicting the Mott-Hubbard insulators and charge-transfer insulators: (a) Mott-Hubbard insulator in the large-U limit; (b) charge-transfer insulator in the large-U limit; (c) charge-transfer type correlated electronic states in real materials, here the doping induced d-p correlated electronic states are considered, near Fermi level, the Zhang-Rice singlet band emerges. UHB represents upper Hubbard band. LHB represents lower Hubbard band. CTB represents charge-transfer band. ZRSB represents Zhang-Rice singlet band, E_F represents Fermi level and Δ denotes the charge-transfer gap.

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图 4 一些不同超导对称性的配对能隙函数投影到La₃Ni₂O₇费米面上的图示　(a) s_±波, (b) ${\mathrm{d}}_{x^2- y^2} $ + is_±波, (c) ${\mathrm{d}}_{x^2- y^2} $波, 红色表示正的配对能隙符号, 蓝色表示负的配对能隙符号, 白色代表配对能隙为零的节点区域; 注意当系统有多种不同实空间电子配对键(pairing bonds)共存时, 能隙函数可能会比图示的更复杂, 能隙节点的位置也可能变化^[109]

Figure 4. Projection of pairing gap functions with different symmetries onto the Fermi surface of La₃Ni₂O₇: (a) s_±-wave, (b) ${\mathrm{d}}_{x^2- y^2} $ + is_±-wave, (c) ${\mathrm{d}}_{x^2- y^2} $-wave; here warm colors represent positive pairing gap sign, and cool colors represents negative pairing gap sign, the white regions denote gap nodes where pairing gap vanishes. Note that the gap function may become more complicated than illustrated, when multiple real-space electron pairing bonds coexist, potentially altering the positions of the gap nodes^[109].

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Vol. 74, Issue 17 - 2025-09-05

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Recent advances and prospects in theoretical study of bilayer nickelate superconductor La₃Ni₂O₇