Newly Discovered FeAs-Superconductors: Opportunity and Challenge

2008.5.16 Peking University

Z. D. Wang (汪子丹）

The University of Hong Kong

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

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)

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

High-Tc Copper-Oxides

Crystal structure of La2CuO4 Schematic of CuO2 plane

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

Schematic Phase Diagram

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.

Crystal Structure of LaOFeAsF

Experimental Results (II)

SDW in the normal state

Neutron scattering data Reflective Optical Spectroscopy

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.

Unconventional SC

Experimental Results (IV)

Symmetric Phase Diagram (Electron-doping vs hole-doping)

Tc vs TF_of unconventional superconductors (grey region)

Band Structure Calculations (LDA, DMFT)

LDA (nonmagnetic structures)

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.

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)

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

Origin of the SC Pairing

21'

'21' iiHiil

ilili JnnUnnUH σσσσ

σσσ

σσrr

•++= ∑∑

Intraband AF fluctuation Intraband d-wave SC

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).

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

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.

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

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

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,

Phase Diagram

Zero-bias Coherent Peak

Nodal d-wave pairing(two gaps behavior)

Useful Relations

II. FLEX Results

Microscopic Model Hamiltonian

Two-band structure in the reduced (original) BZ

Fermi pockets in theextended BZ

Fermi pockets in the BZ

Spin susceptibility

Superconducting pairing

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?

Thank you!