Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer...
Transcript of Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer...
Superconductivity beyond the dimer model in 2Dorganic charge transfer salts
Michaela Altmeyer, Daniel Guterding, Harald O. Jeschke, andRoser Valentı
Institut fur Theoretische Physik
March 5, 2015
SFB/TR 49
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Organic charge transfer salts:Crystal structure and properties of (ET)2X
ET = BEDT-TTF= bis(ethylene-dithio)-tetrathiafulvaleneis the electrondonor
X is the electronacceptor (e.g.Cu(NCS)2)
we concentrate onκ-(ET)2X salts
AFI to SCtransition withpressure orvariation of X Figure : Muller, ChemPhysChem 12, 1222 (2011)
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Organic charge transfer salts:Electronic structure of κ-(ET)2X
two donor moleculestransfer in total oneelectron to theacceptor X
two-dimensionalelectronic structure inthe ET-plane
four ET molecules inthe unit cell, 3/4filled four-band model
effective model onlydescribes dimers ofET molecules, 1/2filled two-band model
Figure : Ferber, Foyevtsova, Jeschke, Valentı, PRB 89, 205106
(2014)
-0.5
-0.25
0
0.25
M X Γ Y M Γ Z
E (
eV
)
-π
0
π
-π 0 π
ky
kx
Figure : κ-(ET)2Cu(NCS)23 / 7
Symmetry of superconducting pairing in κ-(ET)2X
Ab-initio calculations
full potential local orbital (FPLO) code
molecular orbital models from projectiveWannier functions
Superconductivity calculations
RPA spin-fluctuation pairingBickers, Scalapino, White, PRL 62, 961 (1989)
Graser, Maier, Hirschfeld, Scalapino, New J. Phys. 11, 025016 (2009)
extract pairing symmetry and relativestrength
0°
20°
40°
60°80°100°
120°
140°
160°
180°
200°
220°
240°260° 280°
300°
320°
340°
kx
ky
TheoryAltmeyer, Guterding, Jeschke, Valentí,
to be published
Schrama et al., PRL 83, 3041 (1999) Experiment
κ-(ET)2Cu(NCS)2
dxy from experiment and theory4 / 7
see also Schmalian, PRL 81, 4232 (1998)
Competing pairing symmetries in κ-(ET)2X
κ-(ET)2Ag(CF3)4(TCE)
leading eigenfunction:71% s˘, 29% dx2´y2
subleading: 100% dxy
s+-
qy
qx
qy
qx
dx2-y2
s+-/dx2-y2
dxy
qx
qyπ
-π
0
-π 0 π
Δ [a
rb. u
nits
]
5 / 7see also Schmalian, PRL 81, 4232 (1998); Kuroki et al., PRB 65, 100516(R) (2002)
Material dependence of Tc in κ-(ET)2X
λ measures pairing strength
U is material dependent
feature rich spin-susceptibility notdiscussed in previous work
0
4
8
12
16
0
0.2
0.4
0.6
0.8
1
Tc [
K]
λ
U = const.Tcλ
4.8
5.2
5.6
6
6.4
κ-(ET)2 Ag(C
F3 )
4 (TCE)
α1 ’-κ-(ET)
2 Ag(CF3 )
4 (TCE)
α2 ’-κ-(ET)
2 Ag(CF3 )
4 (TCE)
κ-(ET)2 C
u(NCS)
2
κ-(ET)2 C
u[N(C
N)2 ]Br
U/t
actual U/t ratioU/t
Kuroki et al., PRB 65, 100516(R) (2002)
Altmeyer, Guterding, Jeschke, Valentí, to be published
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Summary
we derived ab-initio models for many κ-phase materials
RPA spin-fluctuation pairing yields s˘{dx2´y2 or dxy gap
material dependence of Tc comes out correctly
no simple dependence on microscopic parameters
7 / 7Altmeyer, Guterding, Jeschke, Valentı, to be published
Conversion from four-band to dimer model
t “ 12pt2 ` t4q
t 1 “ 12t3
U “ 2t1
Figure : Kandpal et al., PRL 103, 067004 (2009)
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Tight binding+RPA formalism in a nutshell
χpqst p~qq “ ´1
N
ÿ
~k,µ,ν
asµp~kqap˚µ p
~kqaqνp~k`~qqat˚ν p
~k`~qqfpEνp~k` ~qqq ´ fpEµp~kqq
Eνp~k` ~qq ´ Eµp~kq
“
pχRPAspin qpqst
‰´1“ rχpqst s
´1´ pUspinq
pqst
Γpqst p~k,~k1q “
„
3
2Us χ
RPAs p~k´ ~k1qUs `
1
2Us ´
1
2Uc χ
RPAc p~k´ ~k1qUc `
1
2Uc
tq
ps
Γijp~k,~k1q “
ÿ
stpq
at˚i p´~kqas˚i p~kqRe
”
Γpqst p~k,~k1q
ı
apj p~k1qaqj p´
~k1q
´ÿ
j
¿
Cj
dk1‖
2π
1
4π vFp~k1q
”
Γijp~k,~k1q ` Γijp~k,´~k
1q
ı
gjp~k1q “ λigip~kq
Graser, Maier, Hirschfeld, Scalapino, New Journal of Physics 11, 025016 (2009)
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Other interesting talks
talk after next one : Electronic structure of a dual-layeredorganic charge transfer salt, Harald O. Jeschke
Z5.00004 : Generalized bandstructure unfolding method,Friday 11:15 AM, Milan Tomic
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Summary of superconductivity calculations
feature rich spin-susceptibility
RPA spin-fluctuation pairingyields s˘{dx2´y2 or dxy gap
material dependence of Tccomes out correctly
complicated dependence onmicroscopic parameters
s+-/dx2-y2
dxy
qx
qyπ
-π
0
-π 0 π
Δ [a
rb. u
nits
]
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