This talk is devoted to our unforgetable teachers and ... · PDF filePairing in Cuprates and...
Transcript of This talk is devoted to our unforgetable teachers and ... · PDF filePairing in Cuprates and...
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
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