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)

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

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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

]

11 / 7