1. 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

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 2

3. 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
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010

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. 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

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。
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：

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

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

16. 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

17. 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)

18. 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

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

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
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.

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
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

25. 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

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 Series:
Electron doped:
CeO1-xFxFeAs: 41K SmO1-xFxFeAs: 55K
PrO0.89F0.11FeAs: 52K SmFeAsO1-x k, 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 Series: Li(Na)FeAs 16k
d : Sr4V2O6Fe2As2 37K
Iron-Chalcogenide :
a. 11 Series: FeSe, 8k - 37k, FeSexTe1-x
b. 122 Series: K(Cs,Rb)Fe2Se2, 42K 32

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

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

35. 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

36. 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 ?)

37. 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!

38. 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 !

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

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 (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

49. Case 2: Ferropnictides

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

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

52. 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, (2009)

53. Band Structure in Fe-Based Superconductors
Electron and Hole pockets

54. 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, (2008) 54

55. 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).

56. 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

57. Case 3: Ferrochalcogenides

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

59. Minimum Magnetic Model
J1 is Ferromagnetic
J3 is significant and AFM

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

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

62. 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: 62

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

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

65. 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!

66. 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)