1. Sonia Haddad LPMC, Département de Physique, Faculté des Sciences de Tunis (Tunisia) Collaborator Samia Charfi-Kaddour (LPMC, Tunisia) Besma Bellafi (LPMC, Tunisia) STM image, BaFe 1.8 Co 0.2 As 2,J. Hoffman 2010 Superconducting fluctuations as origin of enhanced upper critical fields and Nernst effect in layered superconductors

2. Forget about swimming for a few minutes !!!

3. Motivation Role of superconducting fluctuations on Hc 2 and Nernst coefficient in organic superconductor (TMTSF) 2 PF 6 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 superconductivit y

4. 0 200 600 400 bar 10 20 30 40 Inhomogeneous superconductivity How to obtain it? S. Lefebvre et al. (2000) Chemical substitution Yoneyama et al. (2004).  -(ET) 2 N(CN) 2 Cl C. Pasquier et al. (2007) Hydrostatic pressure N. Joo, Ph.D thesis (2006) SDW/SC SDW Metal Cooling rate (K/mn)

5. 5 C. Pasquier et al. (2007) Inhomogeneous superconductivity How to obtain it? Hydrostatic pressure (TMTSF) 2 PF 6

6. Knebel et al. (2005). Heavy fermions Pure AF phase Coexistence of AF and SC domains Pure SC phase Inhomogeneous superconductivity Universal feature?

7. Pnictides Drew et al. (2008). Inhomogeneous superconductivity Universal feature? SmFeAsO 1-x F x

8. Mixture of insulating and SC phases SC domains ~ 3 nm STM images Lang et al. Nature (2002). Underdoped Bi-2212 Overdoped Bi-2212 Inhomogeneous superconductivity Universal feature? Cuprates

9. Rullier-Albenque, et al, EPL 2008 Disorder Increase of the regime of superconducting fluctuations Inhomogeneous superconductivity Universal feature? Cuprates

10. metal 10 resistivity temperature TcTc Metallic resistivity excess of conductivity Supraconducting regions (Metastable Cooper pairs) resistivity temperatureTcTc Metallic resistivity SC fluctuations appear in the metallic state before the SC transition Inhomogeneous superconductivity Superconducting fluctuations

11. 11 Tc disorder Experiments Abrikosov &Gor’kov Law 0 TcTc T c0 : clean sample T c : dirty sample  : impurity scattering rate Abrikosov and Gor’kov Law: Disagreement Theory-Experiments Inhomogeneous superconductivity Existing theories (zero magnetic field)

12. 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 J0J0 J1J1 J2J2 SC Josephson coupling Insulating Phase s SC d Inhomogeneous superconductivity A Model at zero magnetic field

13. Inhomogeneous superconductivity A Model at zero magnetic field: Results Effect of cooling rate in  - (ET)2Cu[N(CN)2]Br Present model Yoneyama et al. 04’ Abrikosov-Gor’kov law S.H, S. Kaddour, J-P. Pouget, submitted to JPCM Effect of cooling rate on (TMTSF) 2 ClO 4

14. Inhomogeneous superconductivity Inhomogeneous superconductivity and magnetic field ?

15. Inhomogeneous superconductivity Upper critical fields H c2 largely exceeds the Pauli limit H p ~2.5 T in q1D organic superconductors Yonezawa et al. 2008 Lee et al. 1997 Motivation Symmetry SC gap is Singlet (FFLO)? Triplet?

16. 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

17. Superconducting fluctuations: Nernst effect: probe x y z V Transverse voltage E y generated by thermal gradient B B Peltier coefficient  xy = /E y

18. 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

19. Superconducting fluctuations: Nernst effect: existing theories Enhancement of the Nernst effect due to superconducting fluctuations or stripe order

20. Inhomogeneous superconductivity Upper critical fields Model SDW C. Pasquier et al. (2007) d SC Non SC H // a J SC Lee et al. JPSJ (2006)

21. 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 SC NSC H // a T EyEy Peltier coefficient  zy = /E y 

22. 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

23. Superconducting transition temperature Inhomogeneous superconductivity The Model ã = 0 at T c Nc=lB2/02Nc=lB2/02

24. Inhomogeneous superconductivity The Model Nernst coefficient (Self consistent calculations) Peltier coefficient  zy = /E y

25. Inhomogeneous superconductivity Results (H = 0 T) SDW Quasi-1D organic superconductor : (TMTSF) 2 PF 6 C. Pasquier et al. (2007) SC NSC d Experiments pressure

26. Inhomogeneous superconductivity Results (H c2 ) Quasi-1D organic superconductor : (TMTSF) 2 PF 6 Lee et al. (1997) SC NSC d H // a Experiments Superconducting fluctuations increase Enhanced H c2 Present work

27. Inhomogeneous superconductivity Results (H c2 ) Quasi-1D organic superconductor : (TMTSF) 2 PF 6 SC NSC d H // a Experiments Upturn at N c = 0 ( N c = l B 2 /  0 2 ) Lee et al. (1997) Low field high field Present work

28. Inhomogeneous superconductivity Results: Nernst effect (TMTSF) 2 PF 6 Large Nernst effect at T > T c Nernst effect enhanced by Superconducting fluctuation (reducing d/  0 ) (factor 1000) Nernst ? SC fluctuations increase

29. Inhomogeneous superconductivity Results: Nernst effect (TMTSF) 2 PF 6 Nernst ? SC fluctuations increase Nernst effect is enhanced by approaching T c Nernst effect enhanced by Superconducting fluctuations (reducing d/  0 )

30. Inhomogeneous superconductivity Results: Nernst effect (TMTSF) 2 PF 6 SC NSC d H // a Nernst effect is reduced by increasing H Strong decrease as  0 > l B H 1/2 Low field High field

31. Inhomogeneous superconductivity Results: Nernst effect (TMTSF) 2 PF 6 Nernst effect at H> H c2. Large effect for large SC fluctuations T c2 T c1

32. 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

33. SC NSC d Inhomogeneous superconductivity What should be next: 1/ Nernst effect with TDGLT in stripe phase of HTC I. Martin and C. Panagopoulos 2010 2/ After Giamarchi talk’s (Tuesday) Dynamics of domains (Functional RG) (interpretation of Bianconi group’s results cuprates)

34. Acknowledgment Claude Pasquier (Orsay) S. Yonezawa (Kyoto) A. Varlamov (Rome) W. Lang (Wien)

35. Inhomogeneous superconductivity Upper critical fields Motivation Resistivity and specific-heat measurements of H c2 are very different: Resistivity: non saturating H c2 (triplet or FFLO) Thermodynamics: saturating H c2 (singlet) Non saturating H c2 signature of superconducting fluctuations ? (TMTSF) 2 ClO 4 Courtesy of Yonesawa

36. Superconducting fluctuations: Nernst effect: as a good probe Choi et al. PRL. (2005) Wu et al. PRB (2005)