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

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 2

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

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

Conventional Superconductivity

超导现象的发现: Vanishing of Resistivity 0.05 0.10 4.10 4.20 4.30 * 超导的转变温度 T/K R/ 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

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。

超导态基本特性 : ( 2) Flux quantization

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

London’s Equation Gauge Fixed ! Gauge symmetry Breaking!

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.

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

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。 V. Ginzburg L. Landau 自由能表达式： 零场： Imaginary order? Phase and amptitude importance. Kinetic energy vs interaction energy 有场情况： G-L参数：κ=λL/ξ Type-I超导体： Type-II超导体：

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 Imaginary order? Phase and amptitude importance. Kinetic energy vs interaction energy

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 …. Imaginary order? Phase and amptitude importance. Kinetic energy vs interaction energy

Isotropic effect: M 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. Microscopic theory: electron pair: Fermion to boson Energy gap: energy saving Universality Normal state isotopic effect

Energy Saving in superconducting state Microscopic theory: electron pair: Fermion to boson Energy gap: energy saving Universality Normal state isotopic effect Electron kinetic energy was paid in superconducting Total interaction energy was saved in superconducting state Chester: Phys. Rev. 103, 1693 (1956)

BCS理论（1957）：超导电性微观理论 What is superconductivity: Microscopic theory: electron pair: Fermion to boson Energy gap: energy saving Universality Normal state isotopic effect

Quantitative Prediction： Retarded attractive force BCS ratio: Tunneling spectrum Electron Phonon Coupling: Josepheson Effect

Cuprates

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？

To be good and successful Timing Opportunity theorist good problem successful theory 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.

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?

Appealing Differences Cuprates (LaCuO2): 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

Good for superconductor in BCS theory: 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

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?

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

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?

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

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?

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

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 32

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

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

Similarity Between Cuprates and 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

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

Theory of High Tc Superconductivity Should Not be so Fancy! 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!

For any n, it is correct ! 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 !

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

Comparison of Phase Diagrams

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

Case I: Cuprates

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

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

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

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

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!!!

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 Anderson et al, J Phys.Cond. Mat 16 (2004) R755

Case 2: Ferropnictides

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

Magnetic Order in J1-J2 Model J1>2J2 , E=-2J1+2J2 J1<2J2, E=-2J2 AFM Collinear-AFM

Spin wave 1. Spin wave excitation is observed almost in entire zone of reciprocal space. 2. Spin wave excitation is described well by a short-range J1a-J1b-J2 model 3. No clear evidence of stoner continuum J. Zhao et al, Nature Physics 5, 555 - 560 (2009)

Band Structure in Fe-Based Superconductors Electron and Hole pockets

Pairing symmetry in two band-{t}-J1-J2 model + J1 S wave pairing coskx+cosky d wave pairing coskx-cosky J2 coskxcosky sinkxsinky Symmetry factors Function peaks at Fermi surfaces + - + + + + - + + - K. Seo, A. B. Bernevig, J. Hu PRL 101, 206404 (2008) 54

Pairing strength in two band-{t}-J1-J2 model S-wave coskxcosky dominates over other symmetry pairing. There is a small component of dx2-y2 (coskx-cosky). The interband pairing is very small ( only dxy).

Properties of S-wave coskxcosky Pairing Symmetry Order parameters have different signs at electron and hole pockets. S-wave pairing is the strongest if both electron and hole pockets are small and have close sizes! Superconducting gaps are larger in smaller pockets. Fermi surfaces are generally gapped unless heavy doping crosses gapless line. The transition temperature should be very sensitive to J2( explain the dependence of Tc on the angle dependence of structure) - - + + - - Gapless line

Case 3: Ferrochalcogenides

FeTe: Bicollinear Antiferromagnetic State Ferrochalcogenides Magnetism: FeTe: Bicollinear Antiferromagnetic State K0.8Fe1.6Se2: Block AFM

Minimum Magnetic Model J1 is Ferromagnetic J3 is significant and AFM

Phase Diagram FeTe Fe1+yTe BCAF IC1 IC3 IC2 CaFe2As2 AF FM CAF CAF cuprates J.P.Hu, et al, Arxiv:1106.5169

Vacancy Order KFe2Se2: Magnetically driven Magnetic Energy Save: Moment reduction from spin wave Vacancy and Magnetic frustration couple strongly! Chen Fang, et al arXiv:1103.4599

Robust S-wave in KFe2Se2 J1 J3 J2 - + S wave pairing coskx+cosky d wave pairing coskx-cosky J2 coskxcosky sinkxsinky + - J3 Cos2kx+cos2ky cos2kx-cos2ky J1 is ferromagnetic. J3 enhance s-wave pairing C. Fang, et al, arxiv:1105.1135 62

J2 , J3 J1 Curpates: Ferropnictides J1 , J2 Ferrochalcogenites J.P. Hu and H. Ding, arxiv 1107.1334

Prediction of Future High Tc Strong AFM Strong Band Renormalization Collaboration between AFM and Fermi Surface.

Superconducting Gaps Measured from ARPES NdFeAsO0.9F0.1 Ba1-xKxFe2As2 NaFe0.95Co0.05As  BaFe2-xCoxAs2 FeSexTe1-x LiFeAs (K,Cs)Fe2Se2 Almost isotropic gaps around each Fermi pockets. A strong support for local magnetic exchange driving SC ? Determining the pairing symmetry in KFe2Se2 will be critical!

Conclusions: Can we break the last rule of Matthias? High sysmetry is best; Peaks in density of state are good; Stay away from oxygen; Stay away from magnetism; Stay away from insulator; Bernd Matthias The Last Matthias Rule: Stay away from Theorists! Fact: None of superconductor was predicted by theorists! Two Solutions: Convert to a half theorist + a half experimentist Break it ( a task for young generation)