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Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald O. Jeschke, and Roser Valent Institut f ur Theoretische Physik March 5, 2015 1/7

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Page 1: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

Page 2: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

Page 3: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

)

0

π

-π 0 π

ky

kx

Figure : κ-(ET)2Cu(NCS)23 / 7

Page 4: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

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)

Page 5: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

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)

Page 6: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

Page 7: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

Page 8: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

Page 9: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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‖

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

Page 10: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

Page 11: Superconductivity beyond the dimer model in 2D organic ... · Superconductivity beyond the dimer model in 2D organic charge transfer salts Michaela Altmeyer, Daniel Guterding, Harald

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

0

-π 0 π

Δ [a

rb. u

nits

]

11 / 7