（每周三课时），预计开课时间2021年九月 

 A. 开课宗旨 

    The last 15 years have witnessed important progresses in our understanding of the mechanism of superconductivity in the high-Tc cuprates. There is now strong evidence that the strange metal behavior is induced by the quantum critical fluctuation at the pseudogap end point, where the Fermi surface changes its topology from hole-like to electron-like. However, experiments show that the quantum critical behavior in the high-Tc cuprates is qualitatively different from that observed in the heavy Fermion systems and the iron-based superconductors, in both of which the quantum critical behavior can be attributed to the quantum phase transition toward a symmetry breaking phase. The fact that the pseudogap exists as a spectral gap without a corresponding symmetry breaking order, together with the fact that the strange metal behavior occurs as a quantum critical behavior without a corresponding symmetry breaking phase transition, exposes the central difficulty of the field: the lack of a universal low energy effective theory description of the high-Tc phenomenology beyond the Landau paradigm. Recent experiments imply that the dualism between the local moment and the itinerant quasiparticle character of the electron in the high-Tc cuprates may serve as an organizing principle to go beyond the Landau paradigm and may hold the key to the mystery of the pseudogap phenomena and the strange metal behavior. It is the purpose of this course to provide a cohrent introduction to the phenomenology and related physical understanding of the high-Tc cuprate superconductors. 

 B. 本课程的参考书籍与文献 

 近期文献： 

 (1) Scattering and Pairing in Cuprate Superconductors, L. Taillefer, Ann. Rev. Cond. Matt. Phys. 1, 50 (2010).      

 (2) Energy gaps in high-transition-temperature cuprate superconductors, M. Hashimoto, et al.,Nature Physics 10, 483 (2014).

 (3) From quantum matter to high-temperature superconductivity in copper oxides, B. Keimer, S.A. Kivelson, M.R. Norman, S. Uchida and J. Zaanen, Nature 518,179 (2015). 

 (4) Resonant X-Ray Scattering Studies of Charge Order in Cuprates, R. Comin and A. Damascelli, Ann. Rev. Cond. Matt. 7, 369 (2016). 

 (5) A Tale of Two Metals, N. E. Hussey, J. Buhot, S. Licciardello, Rev. Prog. Phys. 81, 052501 (2018). 

 (6) The Remarkable Underlying Ground States of Cuprate Superconductors, C. Proust and L. Taillefer, Ann. Rev. Cond. Matt. Phys. 10, 409 (2019). 

 (7) The Strange Metal State of the Electron-Doped Cuprates, R. L. Greene, et al, Ann. Rev. Cond. Matt. Phys. 11, 213 (2020).

 (8) Leading theories of the cuprate superconductivity: a critique, N. Singh, Physica C:, 580, 1353782 (2020).   

 (9) The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond, D. F. Agterberg, et al., Ann. Rev. Cond. Matt. 11, 231 (2020). 

 (10) Charge ordering in superconducting copper oxides, A. Frano, S. Blanco-Canosa, B. Keimer and R. J Birgeneau, J. Phys.: Condens. Matter 32 374005 (2020). 

(11) A short review of the recent progresses in the study of the cuprate superconductivity，Tao Li, arXiv:2103.13595(an invited review submitted to Chinese Physics B). 

 早期文献： 

(12) Correlated electrons in high-temperature superconductors, E. Dagotto Rev. Mod. Phys. 66, 763 (1994). (13) Pairing symmetry in cuprate superconductors, C.C. Tsuei and J.R. Kirtley, Rev. Mod. Phys. 72, 969 (2000). 

 (14) Angle-resolved photoemission studies of the cuprate superconductors, A. Damascelli, Z. Hussain, and Z.-X. Shen, Rev. Mod. Phys. 75, 473 (2003).

 (15) Quantum- critical theory of the spin- fermion model and its application to cuprates: Normal state analysis, A. Abanov, A.V. Chubukov and J.Schmalian, Advances in Physics, 52, 119 (2003).

 (16) The physics behind high-temperature superconducting cuprates: the 'plain vanilla' version of RVB, P. W. Anderson, P. A. Lee, M. Randeria, T. M. Rice, N. Trivedi and F. C. Zhang, J. Phys: Cond. Matt. 16, R755 (2004). 

 (17) Electrodynamics of high-Tc superconductors, D. N. Basov and T. Timusk, Rev. Mod. Phys. 77, 721 (2005). 

 (18) Doping a Mott insulator: physics of high-temperature superconductivity, P. A. Lee, N. Nagaosa and X.-G. Wen, Rev. Mod. Phys. 78, 17 (2006). 

 相关书籍 

 (19) 铜氧化物高温超导电性实验与理论研究，韩汝珊主编，科学出版社 (2009). 

 (20) d-波超导体，向涛著，科学出版社 (2007). 

 C. 课程时间安排（以下每小节内容约占三个课时） 

 第一章：高温超导研究的概貌 

 1. 超导现象及其研究简史，高温超导的主要物理现象，所涉及的物理问题及其研究意义 

 第二章：高温超导的主要实验研究方法及实验结果的传统理论分析 

 2.朗道理论框架回顾

 3.量子多体系统的线性响应理论，格林函数与自能

 4.输运性质---电导，霍尔响应，热导，磁阻 

 5.热力学性质---比热，熵，磁化率 

 6.角分辨光电子能谱与中子散射谱 

 7.光电导谱与电子Raman谱 

 8.核磁共振谱，扫描隧道谱，RIXS谱以及新的测量手段的发展 

 第三章：铜氧化物高温超导体的基本物性 

 9.高温超导体的材料家族，晶体结构，相图与基本电子结构 

 10.母体材料反铁磁态的基本物性 

 11.d-波超导态的基本物性 

 12.奇异金属态的基本物性 

 13.赝能隙态的基本物性 

 14.赝能隙终止点附近的量子临界行为 

 15.赝能隙区的交织序 

 第四章：铜氧化物高温超导体的微观模型及其主要研究方法 

 16.Hubbard模型，Heisenberg模型与t-J 模型及其基本性质 

 17.高温超导机理的RVB理论 

 18.强关联电子模型的数值研究方法 

 第五章：铜氧化物高温超导机理的一些唯象理论图像讨论 

 19.高温超导体中电子的巡游-局域二元性与自旋-费米子模型 

 20.高温超导体中的超导涨落与预配对 

 21.高温超导体中的电子分数化与拓扑序 

 22.高温超导体中的演生对称性与序的交织 

 23.高温超导体中的量子临界性 

 第六章：高温超导机理研究中的一些开放话题 

 24．全局输运还是准粒子输运？

 25．赝能隙终止点究竟是什么自由度发生量子临界？ 

 26．赝能隙区巨大的热霍尔效应究竟意味着什么？ 

 27．奇异金属区霍尔浓度的线性温度依赖和暗熵行为意味着什么？ 

 28．高温超导体的超导态是BCS形式的吗？ 

 29．高温超导体的超导转变究竟是动能驱动还是势能驱动？ 

 30．光电子能谱的Waterfall结构究竟意味着什么？ 

 31．如何理解电子能谱中广泛存在的non-Drude行为？

 32．电子掺杂和空穴掺杂的高温超导体是否需要采用不同的理论描述？ 

后记： 但愿家人平安，但愿被突然按下的暂停键能重新弹起。