Pairing in Cuprates and Fe-based Superconductors: is it so simple as it is claimed - EPI vs Coulomb pairing mechanism?

M. L. Kulic,

Goethe University Frankfurt/Main, Germany

This talk is devoted to our unforgetable teachers and friends Vitalii Lazarevich Ginzburg and Evgenii Grigorievich Maksimov

2 3 7c

T 100 K ( ) single - band metal Fermi surface

OUTLINE

YBa Cu O

1.

1986 : cuprates SC -

HTSC in cuprates and Fe - based

⇒

2 2x y

0

d x y

1 x xc

d - wave pairing

T 55 K ( ) multi - band metal Fermi surfac

( ) ( )(co

e i 1,2...

s - or s - and d-wave pair

s k cos k )

S

i

F

n

m eAsO F

,

2008 : Fe - based SC -

k

⇒

2

F

ep

1g ?

- similarty of

( ) ( )

phase diagr in cupra

Phonon (EPI) vs spin - f

tes and Fe-based SC

luctuation (SFI) mechanism of pairin

- (band-structure)

ams

DFT EPI is unimpclaims ortant ?

g

!

, ,

2.

k k

e

DFT fails to explain

ARPES, tunneling, phonon line-widths, neutron sctter

0.2!?

- magnetism, phonons, ARPES ........ in both compounds!

- on EPI and SFI!

.

ing make limits

3 Challenge for the pairing

- EPI "dominates" ; Coulomb in scattering in cuprates and Fe-based SC?

- Why robust

lar

nes

in smal

s in both SC?

Pai

gel-q -q

of SC in presence of impurities

. 4

nonmagnetic

theory

Conclusion s

( ) phonons + Coulomb( ) ?ring potential :

equally?: phonon

large-q

interbs( ) + Coulo

sm

and

all-q

intraba m ( )d bn

CUPRATES

Fe - BASED

( Phys.Rep. 338, p.1 (2000) - ) , Advances Cond. Mat. Phys. (2010) - ; M.L.K B1E. G. Maksimov, M.L.K., O. V. Dolgov B2 .

CUPRATES → YBCO – prototype of HTSC material

; 93 KcT 2 3 7YBa Cu O

2 3 6 - due to strong correlations

d-wave pairing importance of magnetism for pairing?

importance of ph

xYBa Cu O

AF - order and Mott - insulator

ionic - metallic structure onons!

?HTSC is due to phonons or Coulomb (spin - fluctuations) or both

one-band Fermi surface

Fe-based superconductors → LaOFFeAs – prototype for ferro-pnictides

( )KT

1 ( ) ( )

50 100 even in best !

- (defects) for sign changing of ( ),

like d-wave and !?

- why is SC in Fe-based robust agains

nonmagnetic impurities detrimental

imp

imp

T T

cm

s

single crystals

k

t the nonnagnetic impurities?

Fe

As

hole pocket

electron pocket

multi-band Fermi surface

- pairing?

s

Inelastic magnetic neutron scattering against SFI mechanism

91 cT K

92.5 cT K

Big Change in but Small Change in !

Ph. Bourges et al. (1999)

cIm T

( , ) Q

70 80

2

0

~ exp{ 1/ }

Im ( , )~ small !

c sf sf

meV

sf sf c

T

Qg d T

SFI-theory assumes too large (0.7 1) ! sfg eV

How Im ( , ) behaves with increase of ?Q

Inelastic X-ray scatt., N.Le. Tacon (2011)

Im ( 0.3, ) peak at =250 meV ! q

Neutron scatt. M. Fujita et al (2012)

Im( , ) drops with increasing ! dq q

~ exp{ 1/ }

= + ?

c sf sf

low high

sf sf sf c

T

T

S

What about phonons and EPI?

FI solely can not give high T !? c

ARPES in 4-layered HTSC against SFI

2 3 4 8 1 2Ba ( )Ca Cu O O F

Y. Chen et al. (2006)

60

2 !!

against SFI!

P

N

cT K

Failure of DFT for Phonon spectra in cuprates

Cuprates: DFT underestimates phonon line-widths by factor 10-20!

Bond-stretching (longitudinal) mode

2

2

Ph ( )~ ( ) Ronon shift: e ( )

Line ( )~ ( ) I-width m ( , ):

ep c

ep c

g

g

q q q,

q q q`0

Sum-rule:

strongly co, 1Im ( , ) (1 )

,

rrelated

LDA-DFT

( 1) -

1

doping

c

q

d q NN

effects (due to ) very important! Many body U W

ARPES kink at the nodal (N) -point

( ) (

( ) )

m

(

)

ax

2

Puzzle:

isotropic EPI theory predicts:

FSP in (

, ) !

s n

kink ki

s n

kink kin

k

k

n

F

q

kink

A. Lanzara et al. (2001)

max

( ) 0

( )

N

A

k

k

In fact all phonons contribute to !cT

D. Shimada eta al. (1997, 2007)

Tunneling vs phonon Raman spectra in LASCO films

H. Shim et al. (2008)

Constraints on EPI imply strong q-dependence

epi forward scattering peak ( ) in EPI ( )qWay out FSP

3 ( )( ) ( , ) ( , ) ( , )

2

( , ) ( )[cos cos ] and ( ) 1

sfi

c

x y epi

dZ d q V th

T

k k Z i

q

k k - q q

k

(400-1100) !sfi

coT K

: pairing is due to EPI is pair-breakingAsuumption SFI

0

1 1 ln ( ) ( )

2 2 2

epic

sfi

c c

T

T T

2epi epiT

- for 160 cT K

Question - how large is the ?sfi

coTbare

0

i

tr tr

pairing ( ) ( )(cos cos )

2. high 160

3. rather coupling =1- 2

4. 0.4 0.6 ( (T) )

x y

c

ep

1. , k k

T K

T

d - wave

large EPI

small

k

Experiment EPI must be strongly momentum dependent

0 ( , )(

, )( )

ep

c

g

k qk q

q

0 ( , )(

, )( )

ep

c

g

k qk q

q

0

Long range EPI ( ) due to:

( , )- long range due to

( )

- long range due to ( , ) (vertex)

ep

c

forward scattering peak

gthe Madelung energy

strong correlations q

k q

q

k

*

1

( )

* * ( ) ( )

- since and

i

i ii

c ph

d s

d d d s c c

T e

T T

1 3 s d

EPI strongly -dependent

Theory: strong correlations EPI peake

Experim

d at small !

ents

k

k

: =0adiabatic : 0adiabaticnon

21:28 14

epi in with 18 K 1 !?cARPES LiFeAs T

2 3( )

10

(1,2,3)

( ) 2 1.38

0.75; 0.25; 0.38

- it is not sufficient to explain ?

- additional coupling is needed ?

ep ep

ep

c

Fd

T

Failure of DFT for Phonon spectra in Fe-based

2 2BaFe As

As

Fe

2 1

exp !

effects beyond LDA important

?

0.1 (0) 0.4 0.1

0

!

.2

LDA ep

LDA

ep

many body

N cm

Giant magneto-elastic effects

2 2CaFe As

(exp) ( )0.35 but 5 !

- something fails in LDA?

LDA

c cP GPa P GPa

c- at critical pressure : orthorhombic+SDW ( 0) collapsed tetragonal ( 0)P m m

21:28

(?) - many body effectStrong EPI due to large As polarizability

Strong EPI: 4 ( 40 ) ( 1 2 ) !LDA

ep p epV V eV V eV

giant magneto-elastic effects

M.L.K., A. A. Haghighirad, EPL(2008)

. Sawatzky et al. EPL(2009), arXiv:0808.1390G

Magneto-elastic coupling effects

2

0

2

at

31

( ) 16

, ( ) / 2

10 is

c

renc

k p eff

k LDA ren eff k p

p LDA c

P

bP a

c

b b

P due to many body effects!

First order phase transition

M.L.K., A. A. Haghighirad, EPL(2008)

Contribution of EPI to superconductivity

M.L.K., A. A. Haghighirad, EPL(2008)

large pairing

large As isotope effect

with As

1g Strong EPI A - modes

intra - band

Cuprates and Fe-based SC as "two-band" superconductors

hole pocket

electron pocket

2

ma

m

x

ax

( ) 4

2

0, 0, Wishfull properties: - any sign

interba

exp{ 1/ }

Coulomb ( ) und phonons ( ) constructively increasnd intraband

!

!e

c

c

T

T

Robustness of Cuprates and Fe-based SC in presence of nonmagnetic impurities

(I) - ( ) to wiy th ( ) ( ) Two band model k k

( ) (

2

,-1 ( ) ( )

1,2

) ( )

1( ) , ( )( ) ( )

4 ( )

- experiments in Fe-based 200 30 !0

pl i imp inel

i ii ij i i

i i

imp imp imp K

T T TT

kills i gapless unconventional ntraband pairing !

1 1

0ˆ ˆ ˆˆ ˆ( ), ( )

ˆˆ ˆ ˆ( ) [1 ( )]

imp n imp imp n

n loc n

G G i n T i

T i vG i v

M.L.K. S. Drechsler, O.V.Dogov, (2008)

M.L.K., O. V.Dogov, (1999)

0

21

2 2

1 1ln

Scattering: 0, 0

, (0),

[1 ( ) ][1

( ) ( ) 2 2 2

( ) ]2 2

pbc

c

u imp pbpb

c

u pb

v v v v

vn N

v

T

v v v

T

T

Inter - and Intra - Band

*For ( / )=1 and unitary limit

For and unitary limit: (( / ) 1 , 0 a* l so o )0f r

pb

b

u

pv v v v v

v v v

22

1

1

1.94 0.06 2 2 Fermi surface of ( )

nesting SDW instability - peack in ( )

"quasinesting" in SC compounds

pairing due to !?

se

arsenides Ba Fe Co As

s I

h

SF

Q

0.8 2 2Fermi surface of

NO hole pocket no - nesting

no pai ?

he

rng !

selenides K Fe Se

s

Multi-band structure of typical Fe-based SC

exp

exp

in Fe-based: but !

DFT overestimates magnetism: ~ 2 ;

underestimates

(in LaFeAsO)

( DFT in cuprates )

DFT fo

magnetis

~

m :

0.4

r

DFT B

DFT

B

DFT good qualitative bad quantitative predictions

exp "bad" optimized stru ture c

pocket

pock

e

t

elec

hole

tron

2 2

nesting SDW instability - peack in

Tight binding model for

( )

"quasinesting" in SC compounds

pairing du

: fi

e to !?

ve d-orbital

model

s

arsenide BaFe

e h

F

As

s S I

Q

EPI increase orbital fluctu

Orbital fluctuations compet

ations giving rise to

s - H.Kontani(2009)

! No sign change! - H.Kontani(2

e with spin fluct

00

ua ion

9)

t

s pairing

21:28 25

very fragile against impurities

and show magnetic resonance but is

s

s s s

sharper

± ++ s vs s pairing

! multiorbital fluctuations are important

± ++ Transition from s to s in the presence of impurities

multiorbital susceptibility ( ) may be significuntly increased even by small EPI !

favors !

c q

s

: SC due to orbital and spin fluctuations, EPI in first order Assu neglm eption cted

Five d-orbital model – Violation of Anderson‘s theorem for s+- !!

26

1 0.85 0.15 0

exp

In ( ) , 50 ,

( 0.36) 15 , ( 0.75) 0 , 0.5*

For ( 0.05) 250 cm, 42

g=1.5 0.23 and !

x x c

c c

imp c

s

c

Sm Fe Ru AsO F T K

mT x K T x K

m

x T K

g s

cannot survive

0 0.66 [ ] / [ ],*

- for 0.23 0 !

imp c

s s

c c

mg cm T K

m

g g T

S.Onari & H.Kontani, PRL , 177001 (2009)103

1

, , , ,

For :

ˆˆ ˆ ˆ( ) [1 ( )]

ˆˆ ˆ ˆ ˆIn the basis: (1/ )

n loc nT i IG i I

T I N I G T

5 d - orbitals

band k q k q k p p p qp

21:28 27

Coexistence of SC (s++ and s+-) and SDW Problem similar to HTSC (M.L.K et al. (1995))

0(a) - SDW order (r)= cos( ), ( , )

- s-wave SC with =const

ex exh h

Qr Qsign change of ( , )F

k

spectrum ( )E 2 2

k kk

for 0 accidental nodesk

- density of states ( ) (0)

- power law behavior ( )

ex

F

n

h EN E N

v Q

P T T

21:28 28

0(b) - (r)= cos( ), ( , )

- with ( ) ( ) (also !)

ex exh h

SDW order

d - wave SC

Qr Q

k k Q ±holds for s

+

+ +

+

-

-

- -

spectrum ( )E 2 2

k kk

- standard d-wave nodes ( ) 0

- no accidental nodes in ( )

and d-wave SC coexist much easier with SDWs

k

k

sign change of ( , )F

k

1. Pairing in cuprates and Fe-based SCis due to

c

CONCLUSIONS

( ) betw

een EPI and Coulomb

2. In cuprates EPI is important ingredient in pairin

-

g

* d

onstructive interference CI

wave is due to inteplay between EPI and Coulomb

* small-q ("intraband") scattering dominated by EPI

* large-q ("interband") scattering dominated by Coulo

3 In Fe-based SC EPI dominates in intraban

mb

. d pa

* intraband (small-q) scattering due to EPI

* interband (large-q) scattering is probably dominated by Coulomb

4. phenomenon is prereqisite for highe

irin

r

g

?cTCI