This talk is devoted to our unforgetable teachers and ... · PDF filePairing in Cuprates and...
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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
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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 .
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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
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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
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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
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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
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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
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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
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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
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In fact all phonons contribute to !cT
D. Shimada eta al. (1997, 2007)
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Tunneling vs phonon Raman spectra in LASCO films
H. Shim et al. (2008)
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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
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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
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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
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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
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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
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(?) - 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
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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)
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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
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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
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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)
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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
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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
pock
e
t
elec
hole
tron
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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
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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
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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
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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
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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
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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