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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
temperature
Tc
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 sample
a: 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
J2
SC SC SC
SCSCSC
SCSCSC
SC SC SC
SCSCSC
SCSCSC
Josephson coupling
Insulating Phase
20
1 J
s
21,2
1 J
d
s
SCSC
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 model
Yoneyama 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 fields
Model
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
d
Experiments
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
fie
ld
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 fields
Motivation
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)