1. 1 S. Haddad LPMC, Département de Physique, Faculté des Sciences de Tunis, Tunisia S. Charfi-Kaddour LPMC, Faculté des Sciences de Tunis, Tunisia M. Héritier LPS, Orsay, (unité mixte de Recherche) CNRS-Paris XI, France R. Bennaceur LPMC, Faculté des Sciences de Tunis, Tunisia Interplay between SDW and superconductivity in the quasi-one organic superconductor (TMTSF) 2 ClO 4

2. 2 Acknowledgments TheoryExperiments C. Bourbonnais (Sherbrooke) D. Jérome (Orsay) A. G. Lebed (Arizona) Y. Maeno (Kyoto) N. Joo (Orsay)

3. 3 Why quasi-one organic superconductors? (TMTSF) 2 ClO 4 : an exotic organic conductor Effect of disorder on the interplay between Superconductivity and SDW Effect of a magnetic field: new field induced SDW (FISDW) phases

4. 4 Why superconductors ? Uses for superconductors: Also as … Electric generator (99% more efficient than ordinary one) SQUID (Superconducting Quantum Interference Device): sensing weak magnetic field Military: antenna and in detecting mines (US NAVY) … IRM Accelerator LHC (CERN) Maglev in Japan: fast, safe and economic

5. 5 The future of Superconductors

6. 6 Why organic superconductors ? Dream: towards room temperature superconductors !!! Problems: difficulties to synthesize such materials until… Little’s Proposition (1964): look for organic conductors with one dimensional character to get high Tc !!!

7. 7 Why organic superconductors ? But: there are still open questions !!!  1979: discovery of organic superconductivity in a quasi-one dimensional salt (TMTSF) 2 PF 6 (D. Jérome’s group) …then in Bechgaard salts denoted by (TMTSF) 2 X (X=PF 6 -, ClO 4 - …) Interplay between SC/ SDW : coexistence or competition? SDW SC BUT : T C =1.2 K (so low !!!) a complete laboratory for physicists intensive study

8. 8 Needle like Crystal structure of (TMTSF) 2 X TMTSF X TMTSF=tétraméthyl-tétraséléna-fulvalène X= anion: Br -, PF 6 - ; ClO 4 - … c b a

9. 9 a b c Organic chains of TMTSF molecules Conducting planes tbtb tata Key parameters of (TMTSF) 2 X tctc t’ b t c « t b « t a  c «  b «  a quasi-1D conductors

10. 10 1D LL 2D FL Phase diagram of Bechgaard salts AFSC T. Vuletic, et al. Eur. Phys. J. B 25, 319 (2002) (TMTSF) 2 ClO 4 is superconducting at ambient pressure (T c = 1.2 K) ClO 4

11. 11 (TMTSF) 2 ClO 4 : What makes it so special ? TMTSF ClO4 a b c ClO4 anions are noncentrosymmetric 2 possible orientations or

12. 12 (TMTSF) 2 ClO 4 : anion ordering Anion ordering in (TMTSF) 2 ClO 4 ClO 4 TMTSF b c t b Slowly cooled sample (relaxed): ClO4 anions order along b direction at T AO = 24 K Rapidly cooled sample (quenched): ClO4 anions disordered ! V = 0 Periodic potential: V (y) =V cos(  /b y) V: anion potential

13. 13 2V Fermi surface of (TMTSF) 2 ClO 4 k ┴ k Fermi surface of (TMTSF) 2 X without anion ordering Dispersion relation of relaxed (TMTSF) 2 ClO 4 Two-band energy spectrum BB A A

14. 14 Joo et al., Euro. Phys. Lett. 72, 645 (2005) Effect of cooling rate In the quenched samples: pure magnetic state (SDW) Puzzles !!! SC SDW relaxed samples (slowly cooled) : Superconducting (SC) For the intermediate cooling rate: both SC and magnetism.

15. 15 T SC SC/ SDW T SDW Cooling rate T effect of cooling rate: generic phase diagram metal Pure SC Pure SDW

16. 16 Model : Interplay of superconductivity and magnetic phases Anion ordering two band energy spectrum  (k) k A B kFAkFA kFBkFB EgEg Bands separated by gap Eg

17. 17 Method: perturbative renormalization group theory (Bourbonnais et al.) EgEg tbtb system set of coupled chains singlet superconductivity (SSc) CDW SDW triplet superconductivity(tSc)

18. 18 Scattering processes: (g-ology model) g (1) processesg (2) processes m m m m m m m m m m m m m m m m m m mm Most divergent the most dominant fluctuation.

19. 19 E g = 5 K Rapid cooling E g = 8 K Intermediate cooling E g = 15 K Slow cooling Scaling flows of the most divergent t b = 300 K, E F = 2000 K, T cross = 170 K, = 0.6 Singlet SC Coexisting singlet SC/SDW Pure SDW

20. 20 Phase diagram pure singlet SC (SCs) phase (SCs + SDW) pure SDW Limits RG calculations: Is there coexistence or segregation between SC and SDW ? Cooling rate S. Haddad et al. to appear in J. Low Temp. Phys.

21. 21 Experiments Phase segregation ! Ordered ClO 4 region SC SDW Disordered ClO4 region decrease cooling rate (decrease disorder) Next step: compare free energies (pure SC, pure SDW, SC+SDW)

22. 22 Effect of a transverse magnetic field H a b c Organic chains Cascade of field-induced SDW (FISDW) phases

23. 23

24. 24 Other puzzle: Effect of a high magnetic field Generic Temperature field phase diagram in the absence of anion ordering: 2 4 6 8 10 Temperature (K) 510152025 N=0 N=1 2 3 metal Cascade of FISDW phases :already explained within the Quantized nesting model (Lebed, Gor’kov, Maki, Héritier, Montambaux, Lederer). Magnetic field (T) SDW phase inside an original SDW state !!! Temperature field phase diagram in the (TMTSF) 2 ClO 4 (Chung et al. 2000) SDW I SDW III SDW II SDW IV ? ? ? Ok-Hee Chung et al., PRB 61 (2000)

25. 25 2 4 6 8 10 Temperature (K) 510152025 N=0 N=1 2 3 metal Magnetic field (T) High field phases correspond lowest N values Focus on N=0 and N=1 phases

26. 26 G=eHb/hc, b interchain distance In the presence of magnetic field: effective anion gap

27. 27 q1q1 Intraband nesting: N=0 phase Osada et al. (Phys. Rev. Lett. 1992) Interband nesting: N=1 phase  (k)  k AB N=0 Tow nesting vectors N=0 Tow nesting vectors  k AB N=1 one nesting vector N=1 one nesting vector

28. 28 Instability criteria N=0 FISDW phase: Generalized Stoner Criterion Term describing the overlap of the tow SDW components appearing on the two bands Intraband term N=1 FISDW phase: standard Stoner Criterion MFT + RG

29. 29 Thermodynamics: Competition between the N=0 and the N=1 phase F T F1F1 F0F0 T1T1 T0T0 T*1T*1

30. 30 Temperature-field phase diagram Experiments (Chung et al. 2000) ? ? ? Our model S. Haddad et al. Phys. Rev. Lett., 89, 087001 (2002) S. Haddad et al. Phys. Rev B, 72, 085104 (2005)

31. 31 Effect of a parallel magnetic field H a b c Organic chains a Confinement in the (a,b) plane b Free of bird flu !

32. 32 Experiment (Danner et al. 1997) Our model submitted to Eur. Phys. J. B Joo et al. 2006

33. 33 Quantum mechanical calculation Layer index

34. 34 Other models in competition with our !!! Index layer Probability in transverse direction A. G. Lebed, Phys. Rev. Lett. (2005) But, does not explain the resistance behavior

35. 35 What should be next ?  symmetry of the gap in (TMTSF)2ClO4? triplet or singlet ?  Interplay between Superconductivity and SDW : coexistence or competition ? References N. Matsunaga et al. J. Low Temp. Phys. 117, 1735 (1999) A.J. Greer et al. Physica C 400, 59 (2003) N. Joo et al., cond-mat/0507641 S. K. McKernan et al., P.R.L 75, 1630 (1995) O. H. Chung et al., P.R.B 61, 11649 (2000) J. Moser, Ph. D. thesis, Orsay (France) (1999) (unpublished) C. Bourbonnais and L. G. Caron, Int. J. Mod. Phys. B, 5, 1033 (1991) J. Kishine and K. Yonemitsu, J. Phys. Soc. Jpn. 67, 1714 (1998) T. Osada et al. P.R.L. 77, 5261 (1996) S. Uji et al., P.R.B 53, 14399 (1996) H. Yoshino et al., Synth. Met. 133-134, 55 (2003) H. I. Ha et al., cond-mat/0503649 A.G. Lebed et al., P.R.L. 93, 157006 (2004) A.G. Lebed and P. Bak, P.R.B 40, R11433 (1989) T. Osada et al., P.R.L. 69, 1117 (1992) S. Haddad et al., P.R.B 72, 085104 (2005) SDW Sc