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

Superconducting fluctuations as origin of enhanced upper critical fields and Nernst effect in layered superconductors. Sonia Haddad LPMC, Département de Physique, Faculté des Sciences de Tunis (Tunisia). Collaborator Samia Charfi-Kaddour (LPMC, Tunisia) Besma Bellafi (LPMC, Tunisia).

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

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  1. Superconducting fluctuations as origin of enhanced upper critical fields and Nernst effect in layered superconductors Sonia Haddad LPMC, Département de Physique, Faculté des Sciences de Tunis (Tunisia) Collaborator SamiaCharfi-Kaddour (LPMC, Tunisia) BesmaBellafi (LPMC, Tunisia) STM image, BaFe1.8Co0.2As2 ,J. Hoffman 2010

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

  3. Inhomogeneous superconductivity • Experimental facts • Inhomogeneous superconductivity Superconducting fluctuations • Enhancement upper critical fields (layered organic superconductors) • Giant Nernst effect in layered superconductors (organics, HTc, films…) 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)

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

  5. Inhomogeneous superconductivity How to obtain it? C. Pasquier et al. (2007) Hydrostatic pressure (TMTSF)2PF6

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

  7. Inhomogeneous superconductivity Universal feature? Pnictides SmFeAsO1-xFx Drewet al.(2008).

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

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

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

  11. Tc Tc Experiments Abrikosov&Gor’kov Law 0 disorder Inhomogeneous superconductivity Existing theories (zero magnetic field) Disagreement Theory-Experiments Abrikosovand Gor’kov Law: a: impurityscattering rate Tc0: clean sample Tc: dirtysample

  12. J1 Josephson coupling SC SC SC J2 SC SC SC J0 SC SC SC SC SC SC SC SC SC Insulating Phase SC SC SC Inhomogeneous superconductivity A Model at zero magnetic field • 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 SC SC d s

  13. Inhomogeneous superconductivity A Model at zero magnetic field: Results Effect of cooling rate on (TMTSF)2ClO4 Effect of cooling rate in k-(ET)2Cu[N(CN)2]Br Present model Yoneyamaet al. 04’ Abrikosov-Gor’kov law S.H, S. Kaddour, J-P. Pouget, submitted to JPCM

  14. Inhomogeneous superconductivity Inhomogeneous superconductivity and magnetic field ?

  15. Inhomogeneous superconductivity Upper critical fields Motivation Hc2 largely exceeds the Pauli limit Hp ~2.5 T in q1D organic superconductors Symmetry SC gap is Singlet (FFLO)? Triplet? Yonezawa et al. 2008 Lee et al. 1997

  16. Inhomogeneous superconductivity Upper critical fields Motivation Non saturating behavior of H//a (triplet SC FFLO)? Upturn curvature H // a ? Role of the phase segregation? Superconducting fluctuations? Pasquier et al. 2007 Lee et al. 1997

  17. Superconducting fluctuations: Nernst effect: probe B z y V x Transverse voltage Ey generated by thermal gradient B Peltier coefficient axy= <Jxh>/Ey

  18. Superconducting fluctuations: Nernst effect: as a good probe A. Pourretetal. Nature (2006) Giant Nernst effect in fluctuating superconductors Cyr-Choinièreet al. Nature (2009) Y. Wang et al. (2001)

  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 H // a Non SC SC SC SDW d J Lee et al. JPSJ (2006) C. Pasquier et al. (2007)

  21. 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) H // a NSC SC T D Gauge Ey Peltier coefficient azy= <Jzh>/Ey Nernst Geometry

  22. Inhomogeneous superconductivity The Model Method:Time DependentGinzburg-Landau theory Ullah and Dorsey1991, Puica and Lang 2003 Time DependentGinzburg-Landau equation Langevin forces: Superconducting fluctuations

  23. Inhomogeneous superconductivity The Model Superconducting transition temperature ã = 0 at Tc Nc=lB2/x02

  24. Inhomogeneous superconductivity The Model Nernst coefficient (Self consistent calculations) Peltier coefficient azy= <Jzh>/Ey

  25. Inhomogeneous superconductivity Results (H = 0 T) d Quasi-1D organic superconductor : (TMTSF)2PF6 Experiments C. Pasquier et al. (2007) NSC SC SDW pressure

  26. H // a Inhomogeneous superconductivity Results (Hc2) Quasi-1D organic superconductor : (TMTSF)2PF6 d Present work Experiments Superconducting fluctuations increase Enhanced Hc2 NSC SC Lee et al. (1997)

  27. H // a Inhomogeneous superconductivity Results (Hc2) d Quasi-1D organic superconductor : (TMTSF)2PF6 Experiments Present work Lee et al. (1997) NSC SC high field Low field Upturn at Nc= 0 ( Nc= lB2/x02)

  28. Inhomogeneous superconductivity Results: Nernst effect (TMTSF)2PF6 SC fluctuations increase Nernst ? • Large Nernst effect at T > Tc • Nernst effect enhanced by • Superconducting fluctuation (reducing d/x0) (factor 1000)

  29. Inhomogeneous superconductivity Results: Nernst effect (TMTSF)2PF6 SC fluctuations increase Nernst ? • Nernst effect is enhanced by • approaching Tc • Nernst effect enhanced by • Superconducting fluctuations (reducing d/x0)

  30. H // a Inhomogeneous superconductivity Results: Nernst effect (TMTSF)2PF6 d • Nernst effect is reduced by increasing H • Strong decrease as x0 > lB NSC SC Low field High field H1/2

  31. Inhomogeneous superconductivity Results: Nernst effect (TMTSF)2PF6 Tc1 Tc2 • Nernst effect at H> Hc2. • Large effect for large • SC fluctuations

  32. Inhomogeneous superconductivity Summary Model: layered superconductors with slab structure Time Dependent Ginzburg-Landau theory 1/ Upper critical fields are enhanced by superconducting fluctuations induced by the phase segregation 2/ Giant Nernst effect due to SC fluctuations ( good probe) Nernst effect observed in disordered superconductors far form Tc and Hc2

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

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

  35. Inhomogeneous superconductivity Upper critical fields Motivation Courtesy of Yonesawa • Resistivity and specific-heat measurements of Hc2are very different: • Resistivity: non saturating Hc2 (triplet or FFLO) • Thermodynamics: saturating Hc2 (singlet) (TMTSF)2ClO4 Non saturating Hc2 signature of superconducting fluctuations ?

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

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