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)

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)

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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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