Electronic structure and ultrafast dynamics of nickel-based high-temperature superconductors

LI Yidian; YANG Lexian

doi:10.7498/aps.74.20250856

Abstract

Nickel-based superconductors have attracted widespread attention due to their electronic configuration similar to that of copper-based high-temperature superconductors. Recently, the discovery of superconductivity with a transition temperature as high as 80 K in the bilayer nickelate La₃Ni₂O₇ under pressure has not only reignited research interest in nickel-based superconductors but also opened new avenues for the study of unconventional superconductivity. Layered nickel-based superconductors are similar to copper- and iron-based superconductors in crystal structure, superconducting properties, and electronic structure, but they also show significant differences. A deeper investigation into the electronic structure of nickel-based superconductors is expected to reveal the mechanisms behind these similarities and differences, which will further offer critical insights into developing a unified theoretical model and deepen the understanding of unconventional superconductivity. Moreover, the study of nonequilibrium ultrafast dynamics offers new perspectives and regulations for unconventional superconductivity, which has become a vital tool. This paper focuses on the electronic structure and ultrafast dynamics of Ruddlesden-Popper phase layered nickel-based superconductors, systematically reviewing the successful applications of angle-resolved photoemission spectroscopy (ARPES) and ultrafast optical spectroscopy in nickel-based superconductivity research. Specifically, the new properties of different nickelates are compared, including strong electron correlation, Hund coupling, non-Fermi liquid behavior, energy gap formation, and ultrafast electron dynamics. These advances offer important experimental insights into elucidating the mechanisms of unconventional superconductivity and characterizing the properties of their normal states in these materials.

Keywords:

Authors and contacts

Department of Physics, Tsinghua University, Beijing 100084, China

Corresponding author: YANG Lexian, lxyang@tsinghua.edu.cn

Funds: Project supported by the National Basic Research Program of China (Grant Nos. 2022YFA1403100, 2022YFA1403200) and the National Natural Science Foundation of China (Grant No. 12274251).

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Cited By

图 1 常压和高压下R-P相层状镍基氧化物　(a) 单层La₂NiO₄; (b) 双层La₃Ni₂O₇; (c) 3层La₄Ni₃O₁₀的晶格结构; 绿色、灰色和红色小球分别代表La, Ni和O原子, 黑色虚线显示了2层和3层体系中Ni—O八面体沿c方向的取向

Figure 1. Crystal structures of R-P phase layered nickelate oxides at the ambient and high pressure: (a) Monolayer La₂NiO₄; (b) bilayer La₃Ni₂O₇; (c) trilayer La₄Ni₃O₁₀; the green, gray and red spheres represent La, Ni, and O atoms, respectively, the black dashed lines indicate the distortion of the Ni—O octahedra along the c direction in the bilayer and trilayer systems.

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图 2 第一性原理计算的 (a) 常压(AP)和 (b) 高压(HP)下La₃Ni₂O₇的轨道投影的能带结构^[125]; (c) 不同轨道上的电子排布构型示意图^[2]; AB (antibonding band)为反键带, BB (bonding band)为成键带

Figure 2. Orbital-projected band structures of La₃Ni₂O₇ under (a) ambient pressure and (b) high pressure, calculated by density-functional theory (DFT)^[125]; (c) schematic illustration of the electron configurations in different orbitals^[2]; AB represents antibonding band, BB represents bonding band.

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图 3 ARPES测量的常压下La₃Ni₂O₇的能带结构　(a) La₃Ni₂O₇能带结构的三维图示; 沿(b) $ {\bar \varGamma '}\bar{S} $, (c) $ \bar {\varGamma}\bar{X} $和 (d) $ \bar{X}\bar{S} $方向的能带色散; 黄色曲线为经过5倍重整化处理后的密度泛函理论计算的能带结构, 白色虚线为实验中能带色散的视觉引导线, 用于指示轨道选择性的能带重整化^[125], 实验测量温度为18 K

Figure 3. Band dispersions of La₃Ni₂O₇ measured by ARPES at ambient pressure: (a) 3D plot of the electronic structure of La₃Ni₂O₇; band dispersions along the (b) $ {{\bar \varGamma}'}\bar{S} $, (c) $ \bar \varGamma\bar{X} $, and (d) $ \bar{X}\bar{S} $ directions. The yellow curves are the DFT calculated band structure after renormalized by a factor of 5. The white dashed lines are guides to eyes for the experimental band dispersions, indicating the orbital-selective band renormalization^[125]. The experimental temperature is 18 K.

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图 4 (a) DFT计算的La₃Ni₂O₇的三维费米面; (b) 三维费米面的二维投影; (c) 通过ARPES测量的费米面结构, 橙色线条表示常压下单胞的布里渊区, 实验温度为18 K; (d) 使用7 eV激光测量的费米面, 图中叠加了计算的费米面结果作为比较, 实验温度为40 K^[125]

Figure 4. (a) DFT calculated three-dimensional Fermi surface (FS) of La₃Ni₂O₇; (b) two-dimensional projected calculation of three-dimensional FS; (c) FS map measured by ARPES at 18 K, the orange lines are the BZ of the conventional unit cell at the ambient pressure; (d) FS measured using a 7 eV laser at 40 K, the calculated FS is overlaid for comparison^[125].

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图 5 (a)—(c) 理论模拟的La₃Ni₂O₇的光电子谱的对称性, 距原点的距离表示沿费米面特定角度方向的信号强度, LH和LV分别表示水平和竖直偏振, (a) 仅含Ni的e_g轨道的有效紧束缚模型的模拟结果; (b) 实验测得的光电子能谱沿不同方向的强度; (c) 同时包含Ni的e_g轨道和O的p轨道的有效紧束缚模型的模拟结果; (d), (f) (上图)费米面特定动量处的波函数示意图(红色与蓝色表示相对相位, 红/银色球体分别代表O/Ni原子); (下图)利用(a), (c)中对应的模型模拟的ARPES二向色性信号(LV-LH); (e) (上图)实验中光偏振矢量与面内轨道的相对取向; (下图)实测的ARPES二向色性信号^[159]

Figure 5. (a)–(c) Simulated symmetry of photoemission spectra of La₃Ni₂O₇ using linearly vertical (LV) and linearly horizontal (LH) polarization, the distance from the center defines the magnitude of the signal at a given angle along the FS, (a) an effective tight-binding model with only Ni e_g orbitals, (b) experiments, and (c) an effective tight-binding model with both Ni e_g and O p orbitals; (d), (f) (top) schematic illustration of wavefunctions at the indicated momenta along the FS with relative phases in red and blue (O and Ni sites in red and silver, respectively), along with (bottom) the simulated ARPES dichroism (LV-LH) from the same model as in (a), (c). (e) (top) Experimental geometry, showing the polarization vector of the light with respect to the in-plane orbitals, along with (bottom) the experimental dichroism measured by ARPES^[159].

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图 6 (a)—(e) ARPES测量的1313结构的La₃Ni₂O₇高对称方向的能带结构, ARPES谱上方展示了E_F附近的动量分布曲线(MDC), 并标注了对应能带穿越E_F的峰位; (f) 计算的费米面结构, 带撇符号表示重构出的能带^[193]

Figure 6. (a)–(e) ARPES measured band structures of 1313-structured La₃Ni₂O₇ along high-symmetry directions, momentum-distribution curves (MDC) near E_F are shown on top with Fermi crossings marked; (f) calculated Fermi surface structure, the primed symbols corresponds to the reconstructed bands^[193].

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图 7 (a) ARPES测量的La₄Ni₃O₁₀的费米面结构, 布里渊区以绿色实线标出; (b) 使用7 eV激光测量的费米面, 对应(a)图中蓝色虚线区域; (c), (d) 沿$ \bar \varGamma\bar{X} $(c) 和$ \bar \varGamma\bar{S} $方向(d)的能带色散测量结果, (d)中数据沿(a)图中红色虚线标示的方向采集^[144]

Figure 7. (a) Experimental FS of La₄Ni₃O₁₀ measured by ARPES. The BZ is overlaid as indicated by green lines; (b) FS measured with a 7 eV laser corresponding to the blue dashed area in (a); (c), (d) band dispersions along the high-symmetry directions of (c) $ \bar \varGamma\bar{X} $ and (d) $ \bar \varGamma\bar{S} $, data in (d) were collected along the red dashed line in (a)^[144].

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图 8 (a) ARPES测得La₃Ni₂O₇薄膜(左)和块体(右)的能带结构对比^[209]; (b) ARPES测量的La₃Ni₂O₇薄膜不同轨道的能带色散示意图^[210]; (c) ARPES测得的沿布里渊区对角线方向的超导能隙^[211]; (d) ARPES测得的α带对应的能量分布曲线(EDC)的前沿随温度的移动, 表明有超导能隙打开^[212]

Figure 8. (a) Comparison between ARPES measured band structure of La₃Ni₂O₇ thin film (left) and bulk crystal (right)^[209]; (b) ARPES measured band dispersions of La₃Ni₂O₇ thin film with different orbitals characterized^[210]; (c) the superconducting gap along the diagonal of the BZ^[211]; (d) the leading edge shift of energy-distribution curves (EDCs) of the α band at selected temperatures indicating the formation of the superconducting gap^[212].

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图 9 (a) 在Γ-M-X平面(k_z = 0)和 (b) Z-A-R平面(k_z = π)测量的无限层镍氧化物超导体La_0.8Ca_0.2NiO₂薄膜的费米面; (c), (d) 利用107 eV的光子测量的沿M-Γ-M方向(c)和M-X-M方向(d)的能带色散, E_F处的MDC表明了费米穿越的动量位置^[214]

Figure 9. (a) Photoemission intensity map of the infinite-layer nickelate superconductor La_0.8Ca_0.2NiO₂ film at E_F measured at the (a) Γ-M-X plane (k_z = 0) and (b) Z-A-R plane (k_z = π); (c), (d) photoemission spectra along the (c) M-Γ-M direction and (d) M-X-M direction measured using 107 eV photons (k_z = 0), the MDCs at E_F were overlaid to show the Fermi crossings^[214].

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图 10 (a) Pr₄Ni₃O₈的费米面, 图中强调了以布里渊区角落为中心的空穴口袋; (b)—(d) 在温度T = 22 K测量的高对称方向的色散, 紫色线条代表费米能位置处的MDCs, 从MDCs的峰值位置(红点)提取的能带色散重叠在图中^[216]

Figure 10. (a) Fermi surface map of Pr₄Ni₃O₈ which emphasizes the hole pocket centered around the zone corners; (b)–(d) high-symmetry cuts taken at temperature T = 22 K, the purple lines are the MDCs at the Fermi energy, band dispersions extracted from the peak positions of MDCs (red dots) are plotted in the spectra^[216].

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图 11 (a) La₃Ni₂O₇费米面示意图; (b) 沿(a)中Cut1方向测量的能带结构; (c) 来自(b)图的平带γ的EDC堆叠图, 动量范围由(b)图顶部箭头线段标出^[132]

Figure 11. (a) Schematic FS of La₃Ni₂O₇; (b) band structures measured along momentum cuts Cut1 marked in (a); (c) EDC stack of the flat band γ from (b); the momentum region is marked by the arrowed line on top of (b)^[132].

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图 12 由DFT+DMFT方法计算出的(a) La₃Ni₂O₇^[51]和(b) La₄Ni₃O₁₀^[80]常压相动量依赖的谱函数

Figure 12. k-dependent spectral features of (a) La₃Ni₂O₇^[51] and (b) La₄Ni₃O₁₀^[80] in the ambient pressure phase from DFT+DMFT calculations.

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图 13 La₃Ni₂O₇沿$ \bar \varGamma\bar{S} $方向在不同温度下测量的能带色散, 数据采用7 eV激光采集^[125]

Figure 13. Band dispersions of La₃Ni₂O₇ along the $ \bar \varGamma\bar{S} $ direction measured at selected temperatures, data were collected using laser at 7 eV^[125].

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图 14 La₃Ni₂O₇(蓝色曲线)和La₄Ni₃O₁₀(绿色曲线)在常压下随温度依赖的电阻率^[124]

Figure 14. Temperature-dependent resistivity of La₃Ni₂O₇ (blue curve) and La₄Ni₃O₁₀ (green curve) at ambient pressure^[124].

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图 15 (a) La₃Ni₂O₇不同温度下k_F处的EDCs和 (b) EDCs前沿位置的温度演化^[125]; (c) La₄Ni₃O₁₀不同温度下$ \bar \varGamma\bar{X} $方向k_F处的EDCs和(d) EDCs前沿位置的温度演化; (e), (f) La₄Ni₃O₁₀不同温度下$ \bar \varGamma\bar{S} $方向$ {k}_{\mathrm{F}}^{\text{α}} $和$ {k}_{\mathrm{F}}^{\text{β}} $处的EDC曲线^[144]

Figure 15. (a) EDCs of La₃Ni₂O₇ at k_F at different temperatures and (b) corresponding leading-edge position of the EDCs as a function of temperature^[125]; (c) the EDCs of La₄Ni₃O₁₀ at k_F along $ \bar \varGamma\bar{X} $ at different temperatures and (d) corresponding leading-edge position of the EDCs as a function of temperature; (e), (f) temperature-dependent ARPES spectra of La₄Ni₃O₁₀ at $ {k}_{\mathrm{F}}^{\text{α}} $ and $ {k}_{\mathrm{F}}^{\text{β}} $ along $ \bar \varGamma\bar{S} $ at different temperatures, respectively^[144].

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图 16 La₄Ni₃O₁₀温度依赖的瞬态反射率变化ΔR/R　(a) La₄Ni₃O₁₀瞬态反射率数据随温度变化的伪色图; (b) 在选定温度下ΔR/R的典型时间演化曲线, 黑色曲线为对实验数据的唯象拟合结果; 从(b)中提取的反射率变化振幅(c)与弛豫时间尺度(d)的温度依赖关系图, 红线为Rothwarf-Taylor模型的拟合^[124]

Figure 16. Temperature-dependent transient reflectivity changes ΔR/R of La₄Ni₃O₁₀: (a) The false-color plot of temperature-dependent transient reflectivity data of La₄Ni₃O₁₀; (b) typical temporal evolution of ΔR/R at selected temperatures. The black curves are the phenomenological fit to the data; temperature dependence of the (c) amplitude and (d) relaxation time of the transient reflectivity change in La₃Ni₂O₇, red lines represent the fitting to the Rothwarf-Taylor model^[124].

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图 17 (a) 不同温度下La₃Ni₂O₇的瞬态反射率变化; (b) 在选定温度下ΔR/R的典型时间演化曲线, 黑色曲线为对实验数据的唯象拟合结果; (c), (d) 从(b)中提取的反射率变化振幅(c)与弛豫时间尺度(d)的温度依赖性关系图, (d)图中插图为弛豫时间的倒数随温度的演化^[124]

Figure 17. (a) Temperature-dependent transient reflectivity data of La₃Ni₂O₇; (b) typical temporal evolution of ΔR/R at selected temperatures, the black curves are the phenomenological fit to the data; (c), (d) temperature dependence of the (c) amplitude and (d) relaxation time (τ) of the transient reflectivity change in La₃Ni₂O₇, the inset of panel (d) shows the temperature dependence of 1/τ^[124].

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图 18 (a), (b) La₃Ni₂O₇中提取的反射率变化的振幅(a)和弛豫时间(b)随光通量的变化趋势; (c), (d) La₄Ni₃O₁₀中提取的反射率变化的振幅(c)和弛豫时间(d)随光通量的变化趋势, 其中(d)图中的红色曲线为实验数据拟合结果; (a)—(d)中所有数据均在80 K温度下测量获得^[124]

Figure 18. (a), (b) Fluence dependence of the (a) amplitude and (b) relaxation time of the transient reflectivity change in La₃Ni₂O₇; (c), (d) the same as (a) and (b) but for La₄Ni₃O₁₀; the red curve in (d) is the fit to the data; data in (a)–(d) were measured at 80 K^[124]

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图 19 (a) La₃Ni₂O₇和La₄Ni₃O₁₀在室温下测量的532 nm拉曼光谱; (b) 80 K下La₄Ni₃O₁₀的ΔR/R变化, 其中可观察到相干声子振荡. 插图显示扣除单指数背景后的信号振荡部分; (c) 信号振荡部分的傅里叶变换谱, 最主要的声子模频率位于3.87 THz处. 插图为对应的原子振动示意图, 红色箭头表示振动方向(为简化图示, 主要在平面内振动的La原子未予显示); (d) 通过超快反射率和拉曼实验测得的La₄Ni₃O₁₀相干声子频率随温度的变化关系^[124]

Figure 19. (a) 532 nm Raman spectra of La₃Ni₂O₇ and La₄Ni₃O₁₀, measured at room temperature; (b) ΔR/R of La₄Ni₃O₁₀ at 80 K showing the observation of coherent phonon vibrations, the inset shows the oscillatory part of the signal after subtracting the single-exponential background; (c) Fourier transform of the oscillating part of the signal, the most prominent phonon mode locates at 3.87 THz, the inset shows the corresponding vibration of the atoms with the red arrows indicating the vibration directions. For simplicity, La atoms vibrating mainly in the ab plane are not shown; (d) temperature-dependence of the coherent phonon frequency of La₄Ni₃O₁₀ measured using ultrafast reflectivity and Raman experiments^[124].

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图 20 不同压力下测量的温度依赖的泵浦-探测光谱　(a)—(h)分别对应0, 4.2, 8.2, 13.3, 16.7, 19.7, 26和34.2 GPa的压力条件, 各子图中的散点表示提取的弛豫时间常数^[127]

Figure 20. Temperature dependent pump-probe spectra measured at different pressures: (a)–(h) Corresponds to 0, 4.2, 8.2, 13.3, 16.7, 19.7, 26, and 34.2 GPa, respectively. The scatters in each panel are the extracted relaxation timescales^[127].

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

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