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
1 / 7
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)
2 / 7
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
6 / 7
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)
8 / 7
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)
9 / 7
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
10 / 7
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
]
11 / 7