Sonia Haddad

LPMC, Département de Physique, Faculté des Sciences de Tunis (Tunisia)

Collaborator

Samia Charfi-Kaddour (LPMC, Tunisia)Besma Bellafi (LPMC, Tunisia)

STM image, BaFe1.8Co0.2As2 ,J. Hoffman 2010

Superconducting fluctuations as origin of enhanced upper critical fields and Nernst effect in

layered superconductors

Forget about swimming for a few minutes !!!

Motivation Role of superconducting fluctuations on Hc2 and Nernst coefficient in organic superconductor (TMTSF)2PF6

Roadmap

Layered inhomogeneous superconductors +

Superconducting fluctuations (Time dependent Ginzburg-Landau theory)

Experimental facts

Inhomogeneous superconductivity Superconducting fluctuations

Enhancement upper critical fields (layered organic superconductors)

Giant Nernst effect in layered superconductors (organics, HTc, films…)

Inhomogeneous superconductivity

0 200 600400 bar

10

20

30

40

Inhomogeneous superconductivity

How to obtain it?S. Lefebvre et al. (2000)

Chemical substitution

Yoneyama et al. (2004).

k-(ET)2N(CN)2Cl

C. Pasquier et al. (2007)

Hydrostatic pressure

N. Joo, Ph.D thesis (2006)

SDW/SC

SDW

Metal

Cooling rate (K/mn)

5

C. Pasquier et al. (2007)

Inhomogeneous superconductivity

How to obtain it?Hydrostatic pressure (TMTSF)2PF6

Knebel et al. (2005).

Heavy fermions

Pure AF phase Coexistence of AF and SC domains

Pure SC phase

Inhomogeneous superconductivity

Universal feature?

Pnictides

Drew et al. (2008).

Inhomogeneous superconductivity

Universal feature?

SmFeAsO1-xFx

Mixture of insulating and SC phasesSC domains ~ 3 nm

STM imagesLang et al. Nature (2002).

Underdoped Bi-2212

Overdoped Bi-2212

Inhomogeneous superconductivity

Universal feature?Cuprates

Rullier-Albenque, et al , EPL 2008

Disorder

Increase of the regime of superconducting fluctuations

Inhomogeneous superconductivity

Universal feature?Cuprates

10

metal

resistivity

temperatureTc

Metallic resistivity

excess of conductivity

Supraconducting regions(Metastable Cooper pairs)

resistivity

temperatureTc

Metallic resistivity

SC fluctuations appear in the metallic state before the SC transition

Inhomogeneous superconductivity

Superconducting fluctuations

11

Tc

disorder

Experiments

Abrikosov &Gor’kovLaw

0

Tc

Tc0: clean sample Tc: dirty samplea: impurity scattering rate

Abrikosov and Gor’kov Law:

Disagreement Theory-Experiments

Inhomogeneous superconductivity

Existing theories (zero magnetic field)

12

Hypothesis:

1 /Layered superconductor + Josephson coupling (Puica and Lang 03’)

2 /Phase segregation: SC domains embedded in a non-SC matrix+

Josephson couplings between SC domains

J0

J1

J2SC SC SC

SCSCSCSCSCSC

SC SC SCSCSCSC

SCSCSC

Josephson coupling

Insulating Phase

201 Js

a

21,21 J

da

sSCSC

d

Inhomogeneous superconductivity

A Model at zero magnetic field

Inhomogeneous superconductivity

A Model at zero magnetic field: Results

Effect of cooling rate in k-(ET)2Cu[N(CN)2]Br

Present modelYoneyama et al. 04’

Abrikosov-Gor’kovlaw

S.H, S. Kaddour, J-P. Pouget, submitted to JPCM

Effect of cooling rate on (TMTSF)2ClO4

Inhomogeneous superconductivity

Inhomogeneous superconductivity and magnetic field ?

Inhomogeneous superconductivity

Upper critical fields

Hc2 largely exceeds the Pauli limit Hp ~2.5 T in q1D organic superconductors

Yonezawa et al. 2008Lee et al. 1997

Motivation

Symmetry SC gap isSinglet (FFLO)?

Triplet?

Inhomogeneous superconductivity

Upper critical fields

Non saturating behavior of H//a (triplet SC FFLO)?

Upturn curvature H // a ?

Role of the phase segregation?

Superconducting fluctuations?

Lee et al. 1997

Motivation

Pasquier et al. 2007

Superconducting fluctuations:

Nernst effect: probe

x

yz

V

Transverse voltage Ey generated by thermal gradient

B

B

Peltier coefficient axy= <Jxh >/Ey

Superconducting fluctuations:

Nernst effect: as a good probe

Y. Wang et al. (2001)

A. Pourretet al. Nature (2006)

Cyr-Choinière et al. Nature (2009)

Giant Nernst effect in fluctuating

superconductors

Superconducting fluctuations:

Nernst effect: existing theories

Enhancement of the Nernst effect due to superconducting fluctuations or stripe order

Inhomogeneous superconductivity

Upper critical fields Model

SDW

C. Pasquier et al. (2007)

d

SCNonSC

H // a

J

SC

Lee et al. JPSJ (2006)

0,,0 HzA

Gauge

Inhomogeneous superconductivity

Upper critical fieldsModel

Hypothesis:

1 /Superconductor with slab structure + Josephson coupling

2 /Time dependent Ginzburg-Landau Theory

(Ullah and Dorsey 91’ and Puica and Lang 03’ for HTc)

Nernst Geometry

SCNSC

H // aT

Ey

Peltier coefficient azy= <Jzh >/Ey

D

Method: Time Dependent Ginzburg-Landau theory

Langevin forces: Superconducting fluctuations

Time Dependent Ginzburg-Landau equation

Inhomogeneous superconductivity

The Model

Ullah and Dorsey1991, Puica and Lang 2003

Superconducting transition temperature

Inhomogeneous superconductivity

The Model

ã = 0 at Tc

Nc=lB2/x0

2

Inhomogeneous superconductivity

The Model

Nernst coefficient (Self consistent calculations)

Peltier coefficient azy= <Jzh >/Ey

Inhomogeneous superconductivity

Results (H = 0 T)

SDW

Quasi-1D organic superconductor : (TMTSF)2PF6

C. Pasquier et al. (2007)

SCNSC

dExperiments

pressure

Inhomogeneous superconductivity

Results (Hc2)

Quasi-1D organic superconductor : (TMTSF)2PF6

Lee et al. (1997)

SCNSC

d

H // a

Experiments

Superconducting fluctuations increase

Enhanced Hc2

Present work

Inhomogeneous superconductivity

Results (Hc2)

Quasi-1D organic superconductor : (TMTSF)2PF6

SCNSC

d

H // a

Experiments

Upturn at Nc= 0 ( Nc= lB2/x0

2)

Lee et al. (1997)

Low field

high field

Present work

Inhomogeneous superconductivity

Results: Nernst effect

(TMTSF)2PF6

Large Nernst effect at T > Tc

Nernst effect enhanced by Superconducting fluctuation (reducing d/x0) (factor 1000)

Nernst ?

SC fluctuations increase

Inhomogeneous superconductivity

Results: Nernst effect

(TMTSF)2PF6

Nernst ?

SC fluctuations increase

Nernst effect is enhanced by approaching Tc

Nernst effect enhanced by Superconducting fluctuations (reducing d/x0)

Inhomogeneous superconductivity

Results: Nernst effect

(TMTSF)2PF6

SCNSC

d

H // a

Nernst effect is reduced by increasing H

Strong decrease as x0 > lB

H1/2

Low

fiel

d

High field

Inhomogeneous superconductivity

Results: Nernst effect

(TMTSF)2PF6

Nernst effect at H> Hc2.

Large effect for large SC fluctuations

Tc2Tc1

Inhomogeneous superconductivity

Summary

Model: layered superconductors with slab structure

Time Dependent Ginzburg-Landau theory

2/ Giant Nernst effect due to SC fluctuations ( good probe)

Nernst effect observed in disordered superconductors far form Tc and Hc2

1/ Upper critical fields are enhanced by superconducting fluctuations induced by the phase segregation

SCNSC

d

Inhomogeneous superconductivity

What should be next:

1/ Nernst effect with TDGLT in stripe phase of HTC

I. Martin and C. Panagopoulos 20102/ After Giamarchi talk’s (Tuesday)

Dynamics of domains (Functional RG) (interpretation of Bianconi group’s results cuprates)

Acknowledgment

Claude Pasquier (Orsay)S. Yonezawa (Kyoto)

A. Varlamov (Rome)W. Lang (Wien)

Inhomogeneous superconductivity

Upper critical fieldsMotivation

Resistivity and specific-heat measurements of Hc2 are very

different:

Resistivity: non saturating Hc2 (triplet or FFLO)

Thermodynamics: saturating Hc2 (singlet)

Non saturating Hc2 signature of superconducting

fluctuations ?

(TMTSF)2ClO4

Courtesy of Yonesawa

Superconducting fluctuations:

Nernst effect: as a good probe

Choi et al. PRL. (2005)

Wu et al. PRB (2005)