高温超导体的超导机理研究进展 周兴江 中科院物理研究所 超导国家重点实验室 2016/04/28-29 高温与高场超导材料及其应用技术研讨会 上海东郊宾馆 高温超导体的超导机理研究进展 周兴江 中科院物理研究所 超导国家重点实验室

Superconductivity Research: Materials and Mechanism 1987 Break 77K 1931 SC in Alloy 1957 BCS Theory 1978 Heavy Fermion SC 2008 Fe-based HTSC 1981 Organic SC 1962 Josephson Junction 1933 Meissner Effect Tc (Kelvin) 1986 Cu-based HTSC 1911 Discovery of SC 1935 London Theory 1950 GL Theory 1957 Two Types of SCs

Electronic Phase Diagram of Copper-Oxide Superconductors Superconducting state 超导态: Tc 以下； Normal state 正常态: Tc 以上.

BCS Theory for Conventional Superconductivity (1957) Bardeen, Cooper and Schrieffer (1957) Formation of Cooper pairs in the superconducting state; The pairing is mediated by phonons. Consequences: (1). Tc has a limit (~ 40K)—McMillan limit; (2). Superconducting gap is isotropic. D s-wave SC gap

铜氧化物高温超导体的d 波超导能隙对称性 角分辨光电子能谱 相位敏感实验 对能隙大小的测量 对序参量相位的测量 Z.-X. Shen et al., Phys. Rev.Lett.70(1993)1553. H. Ding et al., Phys. Rev. B 54 (1996) R9678 C. C. Tsuei and J. R. Kirtley, Rev. Modern Phys. 72(2000) 969 相位敏感实验 对序参量相位的测量

d-波超导能隙对多晶超导体临界电流的影响 YBCO超导体晶界 D. Dimos et al., Phys. Rev. Lett. 61 (1988) 219; H. Hilgenkamp and J. Mannhart, Rev. Modern Phys. 74 (2002) 485; S. Gfraser et al., Nature Physics 6 (2010) 609.

高温超导机理的解决，对发展新的超导理论，探索新的超导材料以及超导应用有重要意义。 Unusual Superconducting Properties of High-Tc Superconductors d-wave SC gap (1). Tc is high (Tc max= 135K for Hg1223 Tc max =160K under pressure); (2). Superconducting gap is anisotropic. (Electrons are still paired) (1). 电声子相互作用是否仍可能是导致电子配对的原因? (2). 高温超导的配对机理是什么? 高温超导机理的解决，对发展新的超导理论，探索新的超导材料以及超导应用有重要意义。

High Temperature Superconductivity in Cuprates 对凝聚态物理中两个最成功的经典理论提出了挑战：一个是朗道费米液体理论，另一个是BCS超导理论。 高温超导机理的解决，对发展新的超导理论，探索新的超导材料以及超导应用有重要意义。 揭开了“强关联电子体系”研究的全新篇章，为发现新材料、新量子现象和建立新的多体量子理论提供了契机。 高温超导机理被《科学》杂志列为人类未知的125个科学难题之一 “关联电子体系”

高温超导机理:凝聚态物理最具挑战性的物理问题之一 理论上，吸引和汇聚了国际一流著名理论物理学家； 问题的复杂性和艰巨性, 导致理论的多样性和莫衷一是. RVB： P. W. Anderson, T. M. Rice, P. Lee, F.-C. Zhang et al., Spin Fluctuations: D. Pines, D. Scalapino et al., Stripes: S. Kivelson et al., Loop Current: C. M. Varma et al., Phonon and Polarons: N. F. Mott, A. S. Alexandrov et al. ……………. 年轻一代很难进入和有所作为，就像爬山，越往高处，剩下的人越少 高温超导问题的最终解决，不可能依靠理论本身的争论， 而必须取决于决定性 (decisive) 的实验

Science Advances 2, e1501329 (2016)

? High temperature superconductivity still involves electron pairing. Mechanism of High Temperature Superconductivity High temperature superconductivity still involves electron pairing. Origin of the electron Pairing? 1. Glue or not glue? 2. What is the glue? T* ?

传统超导体中BCS理论的实验验证 --隧道实验对超导Eliashberg函数的解析 Tunneling J. Bardeen, Nobel Lecture, 1972. Neutron Scattering F(ω) Theories or Models Simulation Complex Gap Function Schrieffer, Scalapino,Wilkins Phys. Rev. Lett. 10(1963)336. α2F(ω) Eliashberg Equations Inversion McMillan Rowell Phys. Rev. Lett. 14 (1965)108. Giaever, Phys. Rev. 126 (1962)941 It’s generally that one can extract bosonic spectral function in conventional superconductors from the complex gap extracted from tunneling data. What’s the next step we want to do is the same thing as that have been done in traditional superconductors, and we want to extract the bosonic spectral function in high temperature superconductor.

隧道实验不适用于d-波超导体 Eliashberg Equations for d-Wave Pairing： Normal Eliashberg Function Pairing Eliashberg Function A. Sandvik, D. J. Scalapino & N. E. Bickers, Phys. Rev. B 69, 094523 (2004).

角分辨光电子能谱，由于具有动量分辨能力， 超导Eliashberg函数的最有希望的实验手段 成为解析 超导Eliashberg函数的最有希望的实验手段

国际首台真空紫外激光角分辨光电子能谱仪 性能国际领先 光源 观察到以前看不到的新的现象； 开展以前无法开展的工作。 真空紫 外激光 同步辐 周兴江 研究组, 陈创天 研究组,许祖彦 研究组 Guodong Liu et al., Rev. Sci. Instrum. 79 (2008) 023105. （2004年中开始，2006年底完成） 性能国际领先 光源 真空紫 外激光 同步辐 射光源 能量分辨率 (meV) ~1 5~15 动量分辨率 (Å-1) 0.0036 (6.994 eV) 0.0091 (21.2 eV) 光束流强度 (光子/秒) 1014~1015 1012-1013 样品探测深度 (Å) 30~100 (体效应) 5~10 (表面) 观察到以前看不到的新的现象； 开展以前无法开展的工作。

J. M. Bok, H. Y. Choi, C. M. Varma, X. J. Zhou et al., Super-High Precision of Laser ARPES on Bi2212 Data Precision: ~1% J. M. Bok, H. Y. Choi, C. M. Varma, X. J. Zhou et al., Science Advances 2 (2016) e1501329

Normal and Pairing Eliashberg Functions of Bi2212 J. M. Bok, H. Y. Choi, C. M. Varma, X. J. Zhou et al., Science Advances 2 (2016) e1501329

Salient Points and Implications 𝜀𝑁 (𝜃,𝜔) exhibits weak momentum dependence; 𝜀𝑃(𝜔)≈𝜀𝑁 (𝜔) in the superconducting state; The low energy bump grows very significantly below Tc but the rest is independent of temperature. …… These results put strong constraints on superconductivity theories of high temperature superconductors: Phonon; Spin fluctuation; Hubbard model fluctuation; Loop current fluctuation; and more

Superconductivity Mechanism of the Iron-Based Superconductors

铁基超导体--第二类高温超导材料（2008年发现） “11” “111” “122” “1111” FeAs or FeSe Tc~8K Tc~55K J. Paglione and R. L. Greene, Nature Physics 6(2010)645. 铁基高温超导体的超导机理是什么？

General Electronic Structures of Iron-Based Superconductors M X Three hole-like Bands near G; Two electron-like Bands near M. D. J. Singh and M.-H. Du, Phys. Rev. Lett. 100, 237003(2008); I. A. Nekrasov et al., JETP Lett. 88, 144 (2008).

Superconductivity Mechanism of Iron-Based Superconductors --Fermi Surface Nesting? Interband scatterings between hole-like bands near G and electron-like bands near M. G M Superconducting order parameter S+ near G and S- near M (S ) G M K. Kuroki et al., Phys. Rev. Lett. 101, 087004 (2008); I. Mazin et al., Phys. Rev. Lett. 101, 057003 (2008); F. Wang et al., Phys. Rev. Lett. 102, 047005 (2009); I. Mazin, Nature 464, 183 (2010).

First ARPES Measurement of Superconducting Gap in Iron-Based Superconductors (Ba,K)Fe2As2 : Nearly Isotropic H. Ding et al., Europhy.Lett. 83 (2008) 47001 L. Zhao, X. J. Zhou et al., Chin. Phys. Lett. 25(2008) 4402

铁基超导体(Ba,K)Fe2As2近各向同性的超导电性 H. Q. Yuan et al., Nature 457 (2009) 565.

Distinct Fermi Surface Topology in Iron-Based Superconductors T. Qian et al., PRL 106, 187001 (2011). Y. Zhang et al., Nat. Mater. 10, 273 (2011). D. X. Mou et al., PRL 106, 107001 (2011). L. Zhao et al., PRB 83, 140508(R) (2011). D. F. Liu et al., Nat. Commun. 3, 931 (2012). S. L. He et al.,Nat. Mater. 12, 605 (2013). S. Y. Tan et al.,Nat. Mater. 12, 634 (2013). L. Zhao et al., Nat. Comm.7,10608(2016). X. H. Liu et al., PRB 92, 060504 (2015).

Implications on Superconductivity Mechanism --Rules out Fermi Surface Nesting Picture If Fermi surface topology is critical, then Hole-Like Fermi Surface near G is NOT important; Electron-Like Fermi Surface near M is crucial. G M

Key Ingredients for the Iron-Based Superconductors 费米面 超导能隙 Extraction of Superconducting Eliashberg Functions? D. F. Liu，X. J. Zhou et al., Nature Communications 3, 931 (2012).

High Superconducting Critical Current of Single-Layer FeSe/SrTiO3 Films W. H. Zhang et al., Chinese Physics Letters 31 (2014)017401.

Summaries Mechanism of high-temperature superconductivity is a prominent problem in condensed matter physics; Its understanding is significant for theory development, exploration of novel superconductors, and application of superconductors. Great progress have been made in understanding the mechanism of high temperature superconductivity, but no consensus has been reached yet. High-precision ARPES can play an important role in understanding the pairing mechanism of high temperature superconductivity.

Thanks

FeSe Single Crystal A. Galluzzi et al., Superconductor Science and Technology 28 (2015)115005.

Examination on Spin Fluctuation Not consistent: The relative magnitudes and functional forms for 𝜀𝑁 (𝑘,𝜔) and 𝜀𝑃(𝑘,𝜔) are quite different for any significant antiferromagnetic correlation length; Momentum dependence. Calculated f2 based on spin-fluctuation Measured f2 C. H.-Y. Hong, Seung Hwang. J.Phys. C 25, 365702 (2013).

Quantum Critical Fluctuations The principal results above are consistent with a theory for the cuprates based on quantum critical fluctuations of the loop-current order. Central paradox : The fundamental physics of the cuprates requires that the same fluctuations which dominantly scatter at angles of ±𝜋/2 in the attractive channel must lead to a nearly angle-independent repulsive scattering in the normal channel.

Extracted Pairing Self-Energy as a Function of Temperature The ~15meV peak : same as normal self-energy. Systematically increase as T decreases below Tc and saturates at low temperature. Weakly 𝜔 dependent.

Possible High Tc in Single-Layer FeSe Film on SrTiO3 20.1meV 9.5meV FeSe/SrTiO3, Tc~80K? C. L. Song et al., Science 332, 1410 (2011). FeSe/Graphene, Tc~8K 2.2meV

Distinct Fermi Surface Topology in Iron-Based Superconductors L. Zhao, X. J. Zhou et al., Nature Communications 7 (2016) 10608.