自旋涨落与非常规超导配对

李建新

doi:10.7498/aps.70.20202180

摘要

铜氧化物高温超导、铁基高温超导、重费米子超导和κ-型层状有机超导等超导体的超导态都与磁性有序态相邻, 且超导能隙在动量空间一般存在变号. 因此, 这些超导体的超导机理被认为有别于常规BCS超导中的电子交换声子导致的各向同性s-波配对. 在这些非常规超导中, 自旋涨落被认为是导致电子形成库珀对的主要起源之一. 本文主要以铜基和铁基高温超导为例简要综述非常规超导中的自旋序和自旋涨落性质, 二维哈伯徳模型中超导的起因及在解释铜基和铁基高温超导配对对称性的应用, 以及与非常规超导紧密相关的中子自旋共振模性质和理论解释. 我们认为, 尽管磁性和超导性的相互影响已经过多年研究, 但仍是当前一个富有挑战的活跃研究领域.

关键词:

Abstract

High-T_c cuprates, iron-based superconductors, heavy-fermion superconductors and κ-type layered organic superconductors share some common features − the proximity of the superconducting state to the magnetic ordered state and the non-s-wave superconducting pairing function. It is generally believed that the Cooper pairings in these unconventional superconductors are mediated by spin fluctuations. In this paper, we present a brief overview on the spin dynamics and unconventional pairing, focusing on high-T_c cuprates and iron-based superconductors. In particular, we will overview the properties of the neutron spin resonance and its possible origin, the pairing mechanism in Hubbard model within the weak-coupling framework and its application to the aforesaid unconventional superconductors. We point out that the interplay between magnetism and superconductivity is still an area of active research.

Keywords:

作者及机构信息

李建新^1,2

1.
南京大学物理学院, 固体微结构物理国家重点实验室, 南京　210093

2.
南京大学, 人工微结构科学与技术协同创新中心, 南京　210093

通信作者: 李建新, jxli@nju.edu.cn

基金项目: 国家重点基础研究发展计划(批准号: 2016YFA0300401)和国家自然科学基金(批准号: 11774152)资助的课题.

Authors and contacts

Li Jian-Xin^1,2

1.
National Laboratory of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, China

2.
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

Corresponding author: Li Jian-Xin, jxli@nju.edu.cn

Funds: Project supported by the National Basic Research Program of China (Grant No. 2016YFA0300401) and the National Natural Science Foundation of China (Grant No. 11774152)

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施引文献

图 1 铜氧化物高温超导La_2–xSr_xCuO₄/Na_2–xCe_xCuO₄、铁基超导Ba_1–xK_xFe₂As₂/Ba(Fe_1–xCo_x)₂As₂、重费米子超导CeCo(In_1–xCd_x)₅以及层状有机超导κ-(BEDT-TTF)₂X (标记为Mott insulator的相区在这里表示反铁磁绝缘体)的典型相图. 图分别来自文献[14,16,23,24]

Fig. 1. Typical phase diagrams for high-T_c cuprates, iron-based superconductors, heavy fermion superconductors and κ-typed layered organic superconductors. The figures are reproduced from Refs. [14,16,23,24].

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图 2 铜氧化物高温超导母体La₂CuO₄的自旋波色散和自旋波强度与二维波矢的依赖关系, 波矢方向见插图. (a)和(c)表示色散, (b)和(d)表示自旋波强度. 其中的实线是线性自旋波理论的计算结果(见文中介绍). 图(a)和图(b)来自文献[35], 图(c)和图(d)来自文献[36]

Fig. 2. (a), (c) Spin-wave dispersion in La₂CuO₄ along high symmetry directions in the two dimensional Brillouin zone as indicated in the inset. (b), (d) Spin-wave intensity as a function of the wave vector. Line is the prediction of the linear spin-wave theory. Fig. (a) and Fig. (b) are reproduced from Ref. [35], Fig. (c) and Fig. (d) from Ref. [36].

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图 3 中子散射实验揭示的掺杂铜氧化物高温超导自旋激发普适色散—沙漏状色散. 图(b)用于比较掺杂和未掺杂体系自旋激发谱的变化, 其中的实线表示未掺杂体系的自旋激发色散(纵轴的单位为meV). 图(a)和图(b)分别来自文献[25]和文献[47]

Fig. 3. The universality of the spin excitations in doped high-T_c cuprates—the hourglass dispersion revealed by neutron scattering experiments. Figure (b) is shown for a comparison with the dispersion in the undoped system, which is represented schematically by the solid lines. The figures are reproduced from Ref. [25] and Ref. [47], respectively.

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图 4 中子散射实验揭示的铜氧化物高温超导YaBa₂Cu₃O_6.6自旋激发在动量空间的分布　(a)激发能$ E = 24\;{\rm{meV}} $; (b)激发能 $ E = 34\;{\rm{meV}} $; (c)激发能 $ E = 75\;{\rm{meV}} $. 其中$ 34\;{\rm{meV}} $对应于自旋共振模能量. 图来自文献[43]

Fig. 4. Images of spin excitations in the momentum space for YaBa₂Cu₃O_6.6 revealed by neutron scattering experiments, at different excitation energies: (a) $ E = 24\;{\rm{meV}} $; (b) $ 34\;{\rm{meV}} $; (c) $ 75\;{\rm{meV}} $. $ 34\;{\rm{meV}} $ is the energy of the spin resonance. Figures are reproduced from Reference [43].

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图 5 铁基高温超导母体BaFe₂As₂沿着$ (\pi, q _{y}) $和$ (q_{x}, 0) $方向的自旋波色散. 图(a)中的实线表示利用各向异性海森伯模型计算的结果, 参数为$SJ_{1 {\rm a}} = 59.2 \pm 2.0,\; SJ_{1 {\rm b}} = -9.2 \pm 1.2,\; SJ_{2} = 13.6 \pm 1.0,\; SJ_{\rm c} = 1.8 \pm 0.3$ meV. 图(a)中的虚线代表利用各向同性海森伯模型计算的结果, 参数为$SJ_{1 {\rm a}} = SJ_{1 {\rm b}} = 18.3 \pm 1.4,\; SJ_{2} = 28.7 \pm 0.5, \;SJ_{\rm c} = 1.8$ meV. 其中S表示自旋. 图来自文献[55]

Fig. 5. Figures show spin wave dispersions in BaFe₂As₂ along the $ (\pi, q_{y}) $ and $ (q_{x}, 0) $ directions, respectively. In the panel (a), the solid line is a Heisenberg model calculation using anisotropic exchange couplings $SJ_{1 {\rm a}} = 59.2 \pm 2.0,\; SJ_{1 {\rm b}} = -9.2 \pm 1.2,\; SJ_{2} = 13.6 \pm 1.0,\; SJ_{\rm c} = 1.8 \pm 0.3$ meV, and the dotted line is that assuming isotropic exchange coupling $SJ_{1 {\rm a}} = SJ_{1 {\rm b}} = 18.3 \pm 1.4,\; SJ_{2} = 28.7 \pm 0.5,\; SJ_{\rm c} = 1.8$ meV. S is the spin of the system. Figures are reproduced from Ref. [55].

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图 6 哈伯德相互作用导致的粒子-粒子通道散射梯型费曼图. 其中的虚线表示哈伯德库仑互作用U　(a)自旋单态通道的散射; (b)自旋三重态通道的散射. 图来自文献[67]

Fig. 6. Ladder Feynman diagram in the particle-particle channel coming from the Hubbard interaction, where the dotted lines denote the Hubbard interaction U: (a) The spin-single channel; (b) the spin-triplet channel. Figures are reproduced from Ref. [67].

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图 7 (a)由(3)式计算的有效电子间相互作用势$ V_{\rm s}({ q}) $沿着四方晶格布里渊区高对称方向的分布. 计算参数为12%空穴掺杂, 并取次近邻跃迁参数$ t' = -0.3 t $和$ U = 2 t $; (b)$ V_{\rm s}({ q}) $经傅里叶变换后在实空间的分布. 图(b)来自文献[67]

Fig. 7. (a) Effective interaction $ V_{\rm s}({ q}) $ between electrons arising from the exchanges of spin fluctuations along the high symmetry directions in the Brillouin zone, calculated by Eq.(3) with the next-nearest-neighbor hopping $ t' = -0.3 t $, $ U = 2 t $ and 12% hole doping; (b) Fourier transformation of $ V_{\rm s}({ q}) $. Figure (b) is reproduced from Ref. [67].

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图 8 利用哈伯徳模型的弱耦合计算方法(方程(3)和方程(5))得到的最有利能隙函数在布里渊区的分布. 其中的粗黑线表示电子费米面, 点线表示配对能隙函数的节点(能隙为零的点). 计算参数基于对铜氧化物高温超导的近似描述, 具体见图7的说明文字. 图来自文献[67]

Fig. 8. The most favorable pairing function obtained from the weak-coupling approach to the Hubbard model Eqs.(3) and (5). The solid lines denote the Fermi surface and dotted lines denote the gap nodes. The parameters are the same as those given in the caption of Fig. 7, which are thought to describe approximately high-T_c cuprates. Figure is reproduced from Ref. [67].

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图 9 (a)自旋激发率$ \chi ({{q}}, \omega = 0) $, (b)电子型能带和(c)空穴型能带上最有利配对函数在动量空间的分布. 这些结果基于对描写铁基超导最简单的两带哈伯徳模型^[75]的弱耦合理论计算^[76]. (d)费米面, 其中$ Q_{\rm{AF}} $表示围绕Γ的空穴费米面与围绕M的电子费米面之间的套叠波矢. 图来自文献[76]

Fig. 9. Momentum dependence of the spin susceptibility $ \chi ({{q}}, \omega = 0) $ (a), the most favorable pairing functions on the electron Fermi pocket (b) and hole Fermi pocket (c). The results are obtained from the weak-coupling approach to the two-band Hubbard model ^[76], which is thought to be the simplest model describing iron iron pnictides ^[75]. (d) The Fermi surface in which $ Q_{\rm{AF}} $ denote the nesting wavevector between the hole pocket around Γ and electron pocket around M. Figures are reproduced from Ref. [76].

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图 10 中子散射实验在(a)铜氧化物超导YBa₂Cu₃O_6.92, (b)铁基超导BaFe_1.85Co_0.15As₂和(c)重费米子超导CeCoIn₅中测量的自旋极化率Im$ \chi ({{q}}, \omega) $与能量的依赖关系. 其中不同符号点标志的曲线表示不同温度的结果. 图来自文献[18,59, 20]

Fig. 10. Spin susceptibility Im$ \chi ({{q}}, \omega) $ measured by neutron scattering on (a) YBa₂Cu₃O_6.92, (b) BaFe_1.85Co_0.15As₂ and (c) CeCoIn₅ for different temperatures below and above the superconducting transition temperature. Figures are reproduced from Refs. [18, 59, 20], respectively.

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图 11 (a)铜氧化物超导YBa₂Cu₃O_6.97, (b)铁基超导Ba_0.6K_0.4Fe₂As₂和(c)重费米子超导Nd_0.05Ce_0.95CoIn₅中自旋共振峰强度随温度的依赖关系. 图分别来自文献[27, 19, 28]

Fig. 11. Temperature evolution of the neutron intensity around the spin resonance in (a) the high-T_c cuprate YBa₂Cu₃O_6.97, (b) iron-based superconductor Ba_0.6K_0.4Fe₂As₂ and (c) heavy fermion superconductor Nd_0.05Ce_0.95CoIn₅. Figures are reproduced from References [27, 19, 28], respectively.

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自旋涨落与非常规超导配对