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
History of Superconductivity
Tc (K)
HgBaCuO
140
TlSrBaCuO
BCS Theory 1957
Ginzburg-Landau
Theory 1950
BiCaSrCu2O9
Josephson
Effect 1962
YBa2Cu3O7
London (two fluid
model) 1934
High Tc SC Theory ?
77
CeFeAsO1-x
55
LaBaCuO4 MgB2
35
26
Onnes 1911
Mercury(Hg)
1910
1920
Meissner effect
1933
1930
1940
V3Si
Nb3Sn
1950 1960
Bednorz &
MÜller
Nb3Ge Cuprates
1986
1970
1980
1990
SrFe2As2
FeSe
Fe-based
2008
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
R/ 
0.10
0.05
零电阻特性
* *
*
*
超导的转
变温度 TC
4.10 4.20 4.30
T/K
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
h
F0 =
2e
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
ns e2 ¶J s ns e2
Ñ ´ Js = B,
=
E
mc
¶t
m
Ñ ´ (Ñ ´ B) = l B
2
ns e 2
Js = A
mc
Gauge Fixed !
Gauge symmetry Breaking!
London’s gap argument
i e *
e2
J =(Y ÑY - YÑY*) - | Y |2 A
2m
m
ÑY = 0
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：
有场情况：
G-L参数：κ=λL/ξ
Type-I超导体：   1 / 2
Type-II超导体：  1 / 2
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
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
….
Isotropic effect:
T  M 1/ 2
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.
Energy Saving in superconducting state
H = Hk + Hv
H k = å Pi,e2 / 2m + å q 2j,l / 2m
i
j
e2
Hv =
[å
+ ...]
4pe 0 ij | ri - rj |
1
•
•
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:
H = å e (k)c c + å (D(k)c c
+
ks ks
ks
+ +
k­ -k¯
k
Y = Õ (m (k) + n (k)c c
+ +
k- -k¯
k
)|0 >
E(k) = e (k) + | D(x) |
2
+ h.c.)
2
Quantitative Prediction：
e
Retarded attractive force
• BCS ratio:
D / kBTc = 1.57
• Tunneling spectrum
2
• Electron Phonon Coupling: a F(w )
• Josepheson Effect
e
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
Good
Timing
theorist
good
problem
•
•
Fundamental questions
Conceptual challenge
Opportunity
successful
theory
•
Identify right problem
• Identify most important
phenomenon
• Ask right question
• Solve it at least selfconsistently
•
•
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
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
Structure of LaOFeAs
Fe
As above
the plane
As below
the plane
Key Question
• Are the Fe-based superconductors
siblings of cuprates?
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
Differences Between Cuprates and Oxypnictides
• Cuprates:
• 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
pairing symmetry
d-wave
Collinear-AFM magnetic order
pairing symmetry
(s-wave ?)
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!
Induction in Math VS Physics
• Mathematical Induction
• Physics Induction
Step 1: n=1, Correct
Step 1: n=1, Correct
Step 2: Assume n=m, Correct
Step 2: n=2, Correct
Step 3: n=m+1, 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
vs.
p-types
La2-xSrxCuO4
Nd2-xCexCuO4
AFM
SC
AFM
Temperature (K)
n-types
SC
Dopant Concentration x
Magnetism
Superconductivity
Case I: Cuprates
Magnetic Order in Cuprates
• Magnetism
J
H  J  Si S j
ij 
a. J>0, Antiferromagnetic
b. Superexchange: kinetic energy saved
c. Between nearest neighbor sites
Cu
O
Superconducting states in curpates
 D-wave
 D-wave
(kx , k y )  (k y ,kx )  Ck Ck  
Form in momentum space
(k )  0 (coskx  cosk y )
 D-wave
configuration in real space: pairing between
two nearest neighbor sites
+
+
-
Pairing Symmetry From Antiferromagnetic Exchange
J  Si S j
ij 
d  (coskx  cosk y )
 J | d |
2
+
-
 J | s |
2
+
+
 s  (cosk x  cosk y )
+
+
+
Which one will win?
Selection Rules of Pairing Symmetry
d  (coskx  cosk y )
+
+
-
J  Si S j
ij 
+
 s  (cosk x  cosk y )
+
+
+
+
 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
~
H  t  Ci C j  J  Si S j
ij 
ij 
A: Doping destroys the long range AFM order
B: Magnetic exchanges provide the force gluing
electron pairs.
a. D-wave pairing is favored over S-wave pairing.
b. 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)
Anderson et al,
J Phys.Cond. Mat 16 (2004) R755
Van Harlingen DJ.
Rev. Mod. Phys, 67, 515, 1995
Case 2: Ferropnictides
Parallel Paradigm of Magnetism in Oxypnictides
Fe
H  J1
As
J1
J2
S S
ij NN
i j
 J2
S S
ij NNN
i j
a. 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
H  J1
S S
ij NN
J1>2J2 , E=-2J1+2J2
AFM
i
j
 J2
S S
ij NNN
i
j
J1<2J2, E=-2J2
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
S wave pairing
coskx+cosky
J1
d wave pairing
coskx-cosky
+
+
+
+
+
-
Symmetry factors
+
-
S wave pairing
coskxcosky
J2
d wave pairing
sinkxsinky
K. Seo, A. B. Bernevig, J. Hu PRL 101, 206404 (2008)
Function peaks at
Fermi surfaces
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
Ferrochalcogenides
• Magnetism:
FeTe: Bicollinear Antiferromagnetic State
K0.8Fe1.6Se2: Block AFM
Minimum Magnetic Model
H = J1
å SS
i
<ij> NN
j
+ J2
å
<ij> NNN
Si S j + J3
å
Si S j - K
<ij> NN NN
• J1 is Ferromagnetic
• J3 is significant and AFM
å (S S )
i
<ij> NN
j
2
Phase Diagram
FeTe
Fe1+yTe
BCAF
IC1
CaFe2As2
CAF
J.P.Hu, et al, Arxiv:1106.5169
IC3
AF
IC2
FM
CAF
cuprates
1
K
Vacancy Order KFe2Se2: Magnetically
driven
(c)
• Magnetic Energy Save:
•Moment reduction from
spin wave
| J1 | +J2 + 2J3
m  0.1B
2J3
d m » 0.4 mB
Vacancy and Magnetic frustration couple strongly!
Chen Fang, et al
arXiv:1103.4599
J3
Robust S-wave in KFe2Se2
S wave
pairing
coskx+cosky
+
+
+
+
J1
+
+
-
S wave
pairing
coskxcosky
J2
S wave pairing
Cos2kx+cos2ky
J3
d wave
pairing
sinkxsinky
D µ coskx cosky - d (cos2kx + cos2ky )
C. Fang, et al, arxiv:1105.1135
d wave pairing
cos2kx-cos2ky
J1 is ferromagnetic.
J3 enhance s-wave pairing
• Curpates:
J1
• Ferropnictides
J1 , J2
• Ferrochalcogenites
J2 , J3
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)