Newly Discovered FeAs-Superconductors: Opportunity and ...
Transcript of Newly Discovered FeAs-Superconductors: Opportunity and ...
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Newly Discovered FeAs-Superconductors: Opportunity and Challenge
2008.5.16 Peking University
Z. D. Wang (汪子丹)
The University of Hong Kong
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OutlineHistorical Review
Preliminary Experimental Results1. High Tc2. SDW at undopped state3. Multiband SC4. Unconventional SC
Existing Theories1. Band Structure calculations: LDA2. Proposed Pairing Symmetry
Our Minimal Model: two-band, d-wave pairing, SDW
Our Microscopic Model and Calculations: intra- and inter band SF fluctuations
Outlook
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Brief historical introduction1911: Onnes discovered superconductivity (Noble Prize)1933: Meissner effect (Meissner & Ochsenfeld)1934: A two-fluid model (London brothers)1950: Ginzburg-Landau theory (G-L)
1957: Type-I and type-II Superconductor (Noble Prize)1957: Microscopic theory of conventional superconductivity (BCS)
(Noble Prize)1962: Josephson effect (Noble Prize)1986: High-Tc superconductors LaBaCuO ( Tc ~ 30K ) (Bednorz & MÜller) (Noble Prize)1987: Y 1 B a2 Cu 3O 7 ( Tc ~ 90K, Wu & Chu)1995-1996: D-wave pairing symmetry2001: MgB2 (Tc ~40K) 2003: NaCoO2 (Tc ~ 5K)2008: Fe-As based high Tc superconductivity
(discovered by Hosono and pushed by Chinese physicists)
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where
)
..(
)(
'''
'''
,
,
kkkkkk
kkkkkkkkk
kk
kk
CCCC
chCCCCV
CCH
↑↓−
∗↑↓−
↑↓−+
↓−+↑
+
−
++
−=
∑
∑ σσ
σμε
kkk CC ↑↓−
∑ ↑↓−−=Δ
'''''
kkkkkk
CCV
Microscopic BCS Theory for Conventional Superconductivity
is the Cooper pairing, whose order parameter
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High-Tc Copper-Oxides
Crystal structure of La2CuO4 Schematic of CuO2 plane
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Main UnderstandingsDoped Mott InsulatorsMain Physics in CuO2 PlanesStrong electronic correlationAFM spin correlationSuperconducting state: rather normal; while normal state: abnormal;An Acceptable Microscopic theory is still awaited
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Schematic Phase Diagram
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Fe-As SC: Experimental Results (I)
Higher TcElectron-doped Materials:
LaO0.9F0.1FeAs 26K CeO1-xFxFeAs 41K, SmO1-xFxFeAs 43KPrO0.89F0.11FeAs 52K, …ReFeAsO1-x 55K
Hole-doped Materials:La1-xSrxOFeAs 25K, etc.
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Crystal Structure of LaOFeAsF
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Experimental Results (II)
SDW in the normal state
Neutron scattering data Reflective Optical Spectroscopy
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Experimental Results (III)
Multiband Effect
Temperature dependence of Hall resistivitywas observed which may suggest a strong multiband effect in the electron-doped and hole-doped samples.
The lines corresponds to Bc2(T) calculated from the two-gap theory.
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Unconventional SC
Experimental Results (IV)
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Symmetric Phase Diagram (Electron-doping vs hole-doping)
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Tc vs TF_of unconventional superconductors (grey region)
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Band Structure Calculations (LDA, DMFT)
LDA (nonmagnetic structures)
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Proposed Pairing Symmetry
Extended s-wave Spin-triplet p-waveSpin-triplet orbit-singlet s-wave
Extended s-wave: FS pockets located around Γand around M, SC order parameterson the two sets of the FSs have the opposite signs.
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Our Work and Main Findings
The normal state has an SDW order (Q=(π,π)), while upon the charge carrier doping the SDW order drops rapidly and the SC order emergesdue to the two-band (electron and hole) SC nature of the material, Tc as a function of the effective doping density shows a nearly symmetric electron-hole doping dependencetwo-band superconducting state exhibits a d-wave symmetry (SDW fluctuations) Fluctuation-exchange approach on a microscopic two-band model yields quantitative results, supporting strongly our simple effective two-band model
(1) Han, Chen, Wang, EPL 82, 37007 (2008); arXiv: 0803.4346(2) Yao, Li, Wang, arXiv: 0804.4166 (2008)
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Our Minimal Model2-band BCS d-wave pairing + intraband Hubbard interaction
.).( ''
''''
'
12'
'
22'
'
11'
2121
chddccV
ddddVccccV
nnUddccH
kkkk
kk
kkkk
kkkkkk
kk
iiieffk
kkk
kk
kk
kkkk
kk
++
++
++=
↓↑−++
↓↑−++
↓↑−++
++
↓−↑
↓−↑↓−↑
∑
∑∑
∑∑∑σ
σσσσ
σσ
σσ ξξ
)2(02
0)1(01
0
2,1,2,12,1
2,2
/1),4/(1:
ερερ
ρπρ
==
==
eh
eh
nn
WtDOS
Double-degenerated with each for one Fe-sublattice
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Origin of the SC Pairing
21'
'21' iiHiil
ilili JnnUnnUH σσσσ
σσσ
σσrr
•++= ∑∑
Intraband AF fluctuation Intraband d-wave SC
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Origin of SDW OrderCondensate of bound electron-hole pairs “excitons”
∑+
+
−
−−==
k Qkk
Qkkeff
ffQQU
21
21120
120
)()()(),(1
ξξξξ
χχ
577.0,)1(2 21 )
8(71.1
)/(00 ≈−≈−
− −
γεεπ
γ xTW
WUeffSDW SDWeeWW
eW
T
To obtain a simple analytical formula of TSDW , we set m1=m2 and ε1=ε2= ε 0, where the prefect nesting With Q=(π,π) between the two bands occurs at theundoped case (μ=0).
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SDW StateBelow TSDW, the SDW ordering emerges, SDW order parameter is defined as
∑ ⟩⟨=Δ +↓+↑
kQkkeffSDW dcU
2/)(,2/)(,
,2
)()(1
21221122
1
22
QkkkQkkkSDWkk
k k
kkkkeff
ffU
++ +=−=Δ+=Ω
ΩΩ−−Ω+
−= ∑
ξξηξξηη
ηη
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SDW StateCounterpart of Cooper electron-electron pair
4.3/)8(2..150,504350)8(2 1
≈Δ≈=≈Δ −
SDWSDW
SDWSDW
TKsoKTKcmK
).(53.3/2 resultBCSTSDWSDW ≈Δ
According to optical conductivity spectra,
The AF moment/Fe is estimated ~0.31, (exp. ~0.36) ;
TSDW decreases with the shrinkage of lattice.
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SC State
Two band (hole and electron) SC
2
2,1
2,12,1
21
21
2)2/tanh(
, kk k
ck
e
h
e
h
eeeh
hehh TK
KJKJKJKJ
γξξ
∑=⎟⎟⎠
⎞⎜⎜⎝
⎛ΔΔ
=⎟⎟⎠
⎞⎜⎜⎝
⎛ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛At Tc, we have linearized gap equation,
01
1det
21
21 =⎟⎟⎠
⎞⎜⎜⎝
⎛−
−KJKJ
KJKJ
eeeh
hehhNon-zero solution, for Tc
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SC State
General case: Jee,Jhh>0, JeeJhh‡JehJhe>0.
{ JJJJJJJJWnnWnnJJ
whereennnneWW
T
eehhheeheehh
hhh
eee
eff
hehehe
c eff
((((((((
((/)}(
21])
2)2()2(ln
41([1
,)]2)(2([
2/122
2
14/1
+−+−
+−−
=
−−=−
λ
πλ
γ
We obtain,
hheeheehheheeheheeeeehhhhh JJJJJJWWJJJWJJWJJ(((((((((
−==== ,/)(,/,/ 2
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SC State
Special case: JehJhe=JeeJhh.
hheehhee
hh
hhee
ee
hhee
hhee
JJJJJ
hhJJ
J
eeJJJJ
h
e
he
c ennnnWWe
WWT ((((
(
((
(
((
((
+−
+++−
−−=1
])2([])2([)(π
γ
WWJWUWWW eheffhe 05.0,15.0/,3.0/, 2,10 ===== ε
We choose the parameters as,
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Phase Diagram
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Zero-bias Coherent Peak
Nodal d-wave pairing(two gaps behavior)
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Useful Relations
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II. FLEX Results
Microscopic Model Hamiltonian
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Two-band structure in the reduced (original) BZ
Fermi pockets in theextended BZ
Fermi pockets in the BZ
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Spin susceptibility
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Superconducting pairing
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Outlook
1. Origin of Fe-As Superconductivity: electron-electron interaction? If yes, intraband or interband SF fluctuations? Or both? Or doped Mott physics?
2. Pairing symmetry: s-, d-, or p- wave ? To be determined by experiments on single crystals(?)
3. Profound understandings on the above two key points may provide some clue to resolve a long standing issue of copper oxide SC mechanism.
4. Even higher Tc above 77K?5. Novel phenomena and physics? 6. Applications?
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Thank you!