寻找开启高温超导机理的钥匙

1. 寻找开启高温超导机理的钥匙 中科院物理研究所 & 美国普渡大学 胡江平 7／22／2011

2. Acknowledgements Materials: Z.X Zhao, X.R.Chen (IOP), X.H Chen(USTC), H.H. Wen(Nanjing), G.F. Chen(People), F. M. Fang, Z.A Xu (ZJU) … ARPES: H. Ding, X. J. Zhou (IOP) , D. L. Feng (Fudan) …. Neutron: P. C. Dai, S.L Li(IOP), W. Bao(People) STM: Q.K Xue, X. Chen, Y.Y Wang (Tsing), S.H. Pan(IOP) NMR: G.Q. Zheng (IOP), W.Q.Yu (People) Transport: H.Q. Yuan(ZJU), S.Y. Lee(Fudan) Optics: N.L. Wang (IOP), Q.M. Zhang(People) Theory: T. Xiang, Z. Fang, X. Dai (IOP) Z.Y. Wen, G. M Zhang, H. Zai(Tsing), Z.Y. Lu ( People) Q.H. Wang, J.X. Li (Nanjing) J. H. Dai(ZJU), F.C. Zhang(HKU)… Students & Postdoctor: Chen Fang, Kangjun Seo, Wei-Feng Tsai S.A. Kivelson (Stanford), B.A. Bernevig( Princeton), Cenke Xu(UCSB) Lu Yu, D.H. Lee, F. Wang, Q. M. Si

3. History of Superconductivity Tc (K) HgBaCuO 140 TlSrBaCuO BCS Theory 1957 BiCaSrCu2O9 Ginzburg-Landau Theory 1950 Josephson Effect 1962 YBa2Cu3O7 London (two fluid model) 1934 High Tc SC Theory ? 77 CeFeAsO1-x 55 MgB2 LaBaCuO4 KFe2Se2 SrFe2As2 35 Bednorz & MÜller Cuprates 1986 FeSe 26 V3Si Nb3Sn Nb3Ge Onnes 1911 Mercury(Hg) Meissner effect 1933 Fe-based 2008 1940 2010 1920 1990 2000 1910 1950 1960 1980 1930 1970

4. Outline • Theory of conventional superconductors • High Tc Superconductors (cuprates) • Iron-based superconductors and its connections to cuprates The focus of the talk: Conceptual development!

5. Conventional Superconductivity

6. R/ * * * * 0.10 超导的转变温度 0.05 4.10 4.20 4.30 T/K 超导现象的发现: Vanishing of Resistivity 零电阻特性 Heike Kamerlingh Onnes 1908年荷兰物理学家H.开默林－昂内斯液化氦成功，从而达到一个新的低温区（4.2K以下）。 1911年，他发现，当温度降到4.2K附近时，汞样品的电阻突然降到零。他把这种性质称为超导电性。 该工作获1913年诺贝尔物理学奖

7. 超导态基本特性:(1) Meissner effect Walter Hans. Meissner Robert Ochsenfeld Perfect Diamangetic 1933年W.Hans. Meissner 和Robert Ochsenfeld 发现超导体的完全抗磁性，磁化率χ ＝－1，即完全抗磁性，又称为迈斯纳效应。

8. 超导态基本特性: ( 2) Flux quantization

9. London equation （1934） London模型是基于两流体模型的超导宏观唯象理论，引入了London穿透深度（Penetration depth)概念从超导电动力学角度来描述完全迈森纳效应 唯象解释排磁通效应：超导体体内磁通密度为零，使得任意电流流过超导体只能在表面，这会使得表面电流密度无穷大，因而必须引入穿透深度概念。 两流体模型 London穿透深度λ

10. London’s Equation Gauge Fixed ! Gauge symmetry Breaking!

11. London’s gap argument If it is viewed as a single particle, the ground state has a single wavefunction who does not mix with other states when small magnetic field is applied. Therefore, this state must be separated from excited states with an energy gap.

12. London Brother’s Contribution： • Meissner Effect is fundamental property of superconductivity • Superconductivity is a macroscopic quantum phenomenon • Superconductivity state is protected by a gap • Gauge symmetry breaking

13. Ginzburg-Landau theory (1950) 基于Landau二级相变理论的唯象理论，描述Tc附近的现象，想法是要引入一个序参量|Ψ|2=ns/2来的得到自由能的表达式。 L. Landau V. Ginzburg 自由能表达式： 零场： 有场情况： G-L参数：κ=λL/ξ Type-I超导体： Type-II超导体：

14. Ginzburg-Landau theory (1950): order parameter theory • Provide explanation of many properties (thermal, electrodynamic) • Order parameter is complex scalar • Prove superconductivity are macroscopic quantum phenomena • Both phase and amplitude of order parameter are very important • Provide another length scale: coherent length • Predict vortex lattice, type-I and type-II superconductors

15. The Version of Gaps before BCS: • Barden (1930): gap produced by small lattice displacements • CDW gap (Heisenberg, Koppe, 1947): electron wave-packets localized. • SDW( Overhauser): Spin density wave gap • ….

16. M Isotropic effect: Frohlich, 1950: indirect attraction between electrons due to exchange of virtual phonons. Bardeen & Pines, 1955: combined treatment of screened Coulomb repulsion and phonon-induced attraction net interaction at low (w ≲ wD) frequencies may (or may not) be attractive.

17. Energy Saving in superconducting state • Electron kinetic energy was paid in superconducting • Total interaction energy was saved in superconducting state Chester: Phys. Rev. 103, 1693 (1956)

18. BCS理论（1957）：超导电性微观理论 • What is superconductivity:

19. Quantitative Prediction： e Retarded attractive force • BCS ratio: • Tunneling spectrum • Electron Phonon Coupling: • Josepheson Effect e

20. Cuprates

21. 目前：瞎子摸象和战国时代 Is it a good time? 漫漫长夜还是黎明前的黑暗？

22. To be good and successful good problem successful theory Good Timing Opportunity theorist • Identify right problem • Identify most important • phenomenon • Ask right question • Solve it at least self-consistently • Fundamental questions • Conceptual challenge • Quantitative results • Powerful predictions Does not need to be consistent as a theorist even if physics has to be consistent and novel.

23. Fundamental questions • What is superconductivity? • Why do they become superconductors? • What are the fundamental differences between • low Tc and high Tc superconductors? • Why do they become high Tc?

24. Appealing Differences • Complicated lattice structure • Layered structures: Two dimensional • Transition metal: 3d electrons • Strong magnetism • Superconductivity induced by doping • Not a good metal • Very short coherent length • Complicated phase diagram • Low superfluid density • Intrinsic dirty materials • Cuprates (LaCuO2):

25. Conceptual Challenges Good for superconductor in BCS theory: • Normal state: Metal with large density of states • No Magnetism : Magnetism: pairing breaking • Less disorder: especially for d-wave SC • In cuprates and iron-pnictides, all of above conditions are violated and SC is robust: • Bad metal • Strong magnetism • Intrinsic strong disorder

26. Difficulty I: What are the fundamental phenomena • Which phases should we focus on? Superconducting? Normal state: Pseudogap? Strange metal? Insulating state: Magnetism? Hidden competing states? Quantum critical phenomena?

27. Difficulty II: Separating different energy scale • Spin, lattice, orbital, charge: mixed strongly! How to rule out other possibilities?

28. Difficulty III: Lacking of quantitative results • Weak coupling: BCS, physics dominated by electrons near Fermi surface. • Strong interactions: physics is dominated locally. • How to compromise?

29. Good questions ruled out • Novel superconducting state: anyon superconducting (SC breaks time reversal) R.B. Laughlin • Electron Fractionalization in pseudogap state: Fisher and senthil • Kinetic energy saving: Anderson

30. Still working • What causes pseudogap or the nature of pseudogap? • Time reversal symmetry breaking, orbital current states • Relation between magnetism and superconductivity • Is superconductivity state much more normal?

31. What do the iron-based superconductors bring to the high Tc table?

32. Fe-based Supercondcutors Iron-Pnictides: a. 1111 Series: Electron doped: CeO1-xFxFeAs: 41K SmO1-xFxFeAs: 55K PrO0.89F0.11FeAs: 52K SmFeAsO1-x 55k, CaFFeAs:36K Hole Doped: La[1-x]SrxOFeAs ? b. 122 Series: (both Hole and Electron Doped) Ba1-xKxFe2As2, 38K, BaFe2-xCoxAs2 BaFe2As2-xPx, BaFe2-xRuxAs2 ( isoelectronic doping) c. 111 Series: Li(Na)FeAs 16k d. 42622: Sr4V2O6Fe2As2 37K Iron-Chalcogenide : a. 11 Series: FeSe, 8k - 37k, FeSexTe1-x b. 122 Series: K(Cs,Rb)Fe2Se2, 42K

33. Structure of LaOFeAs As below the plane As above the plane Fe

34. Key Question • Are the Fe-based superconductors siblings of cuprates?

35. Similarity Between Cuprates and Oxypnictides • Oxypnictides: • Cuprates (LaCuO2): Transition Metal: 3d electron Layer structure: two dimensions Magnetic ordered state in parent compounds Superconductivity induced by doping Comparable transition temperature (single layer) Very similar phase diagrams Very short coherent length

36. Differences Between Cuprates and Oxypnictides • Oxypnictides: • Cuprates: Fe: 3d6 Cu: 3d9 Spin 1/2 Spin: 0-2 Single d orbits Multi d orbits More complicated band structure Simple band structure Parent compounds: bad metal Parent compounds: insulator Antiferromagnetic Collinear-AFM magnetic order pairing symmetry d-wave pairing symmetry (s-wave ?)

37. Fundamental Questions in High Tc • Why are they high Tc? • Why are the superconducting states so robust? Theory of High Tc Superconductivity Should Not be so Fancy!

38. Induction in Math VS Physics • Mathematical Induction • Step 1: n=1, Correct • Step 2: Assume n=m, Correct • Step 3: n=m+1, Correct • Physics Induction • Step 1: n=1, Correct • Step 2: n=2, Correct • Step 3: n=3, Correct For any n, it is correct !

39. 事不过三 • Curpates • Ferropnictides • Ferrochalcogenites Repeat good things three times: 1 ＝ Maybe 2 ＝ Possible 3 ＝ Infinite ＝ Truth

40. Comparison of Phase Diagrams

41. n-types vs. p-types La2-xSrxCuO4 Nd2-xCexCuO4 Temperature (K) AFM AFM SC SC Dopant Concentration x The Basic Problems in Cuprates Superconductivity Magnetism

42. Case I: Cuprates

43. Magnetic Order in Cuprates • Magnetism J a. J>0, Antiferromagnetic b. Superexchange: kinetic energy saved c. Between nearest neighbor sites Cu O

44. + + - - Superconducting states in curpates • D-wave • D-wave Form in momentum space • D-wave configuration in real space: pairing between two nearest neighbor sites

45. + + + + - + - + Pairing Symmetry From Antiferromagnetic Exchange Which one will win?

46. + + + + - + - + Selection Rules of Pairing Symmetry + • AFM exchange provides pairing force and possible choices of pairing symmetries. • Fermi surface topology selects the pairing symmetry.

47. Local AFM exchange interaction in real space + Fermi Surface topology in reciprocal space • Doping destroys long range AFM order • Doping does not kill short range AFM coupling • Effect of electron-electron correlation • causes strong renormalization Determine High Tc and pairing symmetry!!!

48. Effectiave t-J model A: Doping destroys the long range AFM order B: Magnetic exchanges provide the force gluing electron pairs. • D-wave pairing is favored over S-wave pairing. • D-wave was really a prediction from the meanfield solution of t-J model. D. Scalapino et al, PRB 34 8190 (1986) Kotliar and Liu (1988), Gros, C.(1988) Susumura, Hasegawa and Fukuyama(1988) Yokoyama and Shiba(1988) Afflect,et al (1988) Zhang F.C and T.M.Rice (1988) Van Harlingen DJ. Rev. Mod. Phys, 67, 515, 1995 J Phys.Cond. Mat 16 (2004) R755 Anderson et al,

49. Case 2: Ferropnictides

50. Parallel Paradigm of Magnetism in Oxypnictides Fe As J1 J2 • As bridges four nearest neighbor Fe atoms • b. Two magnetic exchange coupling parameters T. Yildirim, Phys Rev. Lett 101, 057003; F. Ma et al, arXiv: 0804.3370 Q.Si and E. Abrahams, Phys. Rev. Lett 101, 076401 C. Fang et al, Phys. Rev. B 77 224509; C. Xu et al, Phys. Rev. B 78 020501