Haddad - Superconductivity_ Spin

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					Interplay between SDW and superconductivity in
      the quasi-one organic superconductor
                 (TMTSF)2ClO4

                      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       1
                   Acknowledgments



 Theory                         Experiments

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



                                                   2
 Why quasi-one organic superconductors?

 (TMTSF)2ClO4: 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


                                                      3
                      Why superconductors ?

  Uses for superconductors:
                IRM
                                 Accelerator LHC (CERN)




                                    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) …
                                                                            4
Maglev in Japan: fast, safe and economic
The future of Superconductors




                                5
             Why organic superconductors ?

     Dream: towards room temperature superconductors !!!
Little’s Proposition (1964): look for organic conductors with one dimensional
character to get high Tc !!!




    Problems: difficulties to synthesize such materials until…            6
                Why organic superconductors ?

1979: discovery of organic superconductivity in a quasi-one dimensional
salt (TMTSF)2PF6 (D. Jérome’s group)
  …then in Bechgaard salts denoted by (TMTSF)2X (X=PF6-, ClO4-…)




                      BUT : TC=1.2 K         (so low !!!)



    a complete laboratory for physicists                    intensive study


   But: there are still open questions !!!    SDW

                                                                              SC
    Interplay between SC/ SDW:
    coexistence or competition?
                                                                               7
              Crystal structure of (TMTSF)2X




                       TMTSF=tétraméthyl-tétraséléna-fulvalène
                      X= anion: Br-, PF6-; ClO4-…
    Needle like



X                           TMTSF




                               c


       a          b                                         8
        Key parameters of (TMTSF)2X

  Conducting planes                 t’b
                                      tb
                      ta
         c


               b                              tc
    a

    Organic chains of TMTSF molecules



tc « tb « ta       s c « s b« s a          quasi-1D conductors




                                                                 9
           Phase diagram of Bechgaard salts

              1000
                            T ()
                                             1D LL              *
                                                                T

                  100
Temperature (K)




                            M-H                                     METAL




                  10

                            SP AF           SDW
                                                                    2D FL           AF             SC
                   1                                       SC
                                                                                       T. Vuletic, et al.
                        0       10     20    30   40    50          60   70   80 Eur. Phys. J. B 25, 319 (2002)
                                             Pressure (kbar)
                        (TMTTF)2 X                (TMTSF)2 X
                                                        ClO4
                                                         ClO4
                        BF4
                        PF6




                                                  PF6




                  X=
                                  Br




                            (TMTSF)2ClO4 is superconducting                                                       10
                            at ambient pressure (Tc= 1.2 K)
(TMTSF)2ClO4 : What makes it so special ?


                     TMTSF
ClO4
                                     c


                         a
                               b




           ClO4 anions are noncentrosymmetric



           2 possible orientations       or




                                                11
    (TMTSF)2ClO4 : anion ordering
                       Slowly cooled sample (relaxed):

           ClO4 anions order along b direction at TAO = 24 K

    Anion ordering in (TMTSF)2ClO4
                  tb
                                                         Periodic potential:

          c                                          V (y) =V cos( /b y)

                                                         V: anion potential
b
          ClO4           TMTSF



                  Rapidly cooled sample (quenched):

              ClO4 anions disordered !               V= 0
                                                                          12
Dispersion relation of relaxed (TMTSF)2ClO4
    
      
   k  v F  k  kF                                     
                                   4tb cos2 k b  V 2  2tb cos 2k b
                                     2




                                               Two-band energy spectrum
             k┴

                            Fermi surface of
                   2V       (TMTSF)2ClO4




                               k

  A     B      B        A


                              Fermi    surface of
                              (TMTSF)2X without
                              anion ordering

                                                                          13
                        Effect of cooling rate


                                                        Puzzles !!!

          SDW

                                                relaxed samples (slowly cooled) :

                                                      Superconducting (SC)


                                               For the intermediate cooling rate:

          SC                                        both SC and magnetism.

Joo et al., Euro. Phys. Lett. 72, 645 (2005)

                                                    In the quenched samples:

                                                   pure magnetic state (SDW)

                                                                                    14
effect of cooling rate: generic phase diagram

          T


                    metal

                                  TSDW



              TSC                 Pure
                            SC/   SDW
              Pure SC       SDW

                              Cooling rate




                                             15
                     Model :
Interplay of superconductivity and magnetic phases



         Anion ordering        two band energy spectrum



                  Bands separated by gap Eg


                                  (k)

                                               A    B


                                     kFA
                                                        k
                      Eg                      kFB


                                                            16
Method: perturbative renormalization group theory (Bourbonnais et al.)



              system                 set of coupled chains




                                         VM
                          Eg



                                tb




       VM          CDW        SDW
                    singlet superconductivity (SSc)
                                                                         17
                   triplet superconductivity(tSc)
                                     Scattering processes:
                                       (g-ology model)

            g(1) processes                                         g(2) processes
m                  m    m               m             m             m      m             m

    g (1)
      0                      g (1)
                               b                          g (2)
                                                            0                    g (2)
                                                                                   b

m                  m    m               m             m            m       m             m
m                  m    m               m             m              m    m              m

    g (1)
      f                      g (1)
                               t                           g (2)
                                                             t                g (2)
                                                                                f

m                  m    m                             m             m     m              m
                                        m


                    Most divergent V                the most dominant fluctuation.
                                     M




                                                                                         18
                       Scaling flows of the most divergent VM
tb = 300 K, EF = 2000 K, Tcross= 170 K, g (i ) = 0.6
                                          




      Eg = 15 K                                          Eg = 8 K

     Slow cooling                                        Intermediate cooling




             Singlet SC                                     Coexisting singlet SC/SDW




                                   Eg = 5 K

                                  Rapid cooling



                                              Pure SDW
                                                                                        19
           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
                                                                  20
               S. Haddad et al. to appear in J. Low Temp. Phys.
                              Experiments

                           Phase segregation !



           SC         SC
                SDW

             SC


         Disordered ClO4 region

Ordered ClO4 region

                             decrease cooling rate
                              (decrease disorder)


 Next step: compare free energies (pure SC, pure SDW, SC+SDW)
                                                          21
    Effect of a transverse magnetic field

    c                H

        b



a
    Organic chains




                         Cascade of field-induced SDW (FISDW) phases
                                                               22
23
                         Other puzzle: Effect of a high magnetic field

                                                            Temperature field phase diagram in the
                       Generic Temperature field phase        (TMTSF)2ClO4 (Chung et al. 2000)
                       diagram in the absence of anion
                                 ordering:


                  10                                                               SDW I
                                                                                               ?
Temperature (K)




                  8
                                  metal
                  6
                                                                                     SDW III
                   4
                                                  N=0                      ?
                                                                          SDW IV
                                                                                        ?          SDW II
                   2
                                  2   N=1
                             3
                         5        10    15 20       25
                                 Magnetic field (T)
                                                              Ok-Hee Chung et al., PRB 61 (2000)
                  Cascade of FISDW phases :already
                  explained within the Quantized nesting   SDW phase inside an original SDW state !!!
                  model (Lebed, Gor’kov, Maki, Héritier,                                                    24
                  Montambaux, Lederer).
                           High field phases correspond lowest N values



                  10
Temperature (K)




                  8
                                metal
                  6

                  4
                                                N=0
                  2
                                2   N=1
                           3
                                                       Focus on N=0 and N=1 phases
                       5        10    15 20       25
                               Magnetic field (T)




                                                                                     25
In the presence of magnetic field:              effective anion gap




                 4t b 
                v G
         VJ 0          G=eHb/hc, b interchain distance
                 F 




                                                                      26
Osada et al. (Phys. Rev. Lett. 1992)


Intraband nesting:                N=0 phase


Interband nesting:                N=1 phase



         N=0                                         N=1
  Tow nesting vectors                         one nesting vector

             (k)

                              A   B                                    A    B
               q0A
                                                 q1
                                                                  
                                       k                                        k



         B
        q0                                                                 27
                     Instability criteria

                               MFT + RG

 N=0 FISDW phase: Generalized Stoner Criterion

                1 0 m
                                        4 
                                 ( 2)
          1                   1 gb
          ( 2)
                 m Q0 , T     ( 2)
                                       
                                          v ,T 
                                                
         g0     2             2 g0        F    

              Intraband term

                                Term describing the overlap of the
                                 tow SDW components appearing
                                        on the two bands

N=1 FISDW phase: standard Stoner Criterion


                      1    g t( 2 ) 
               1
               ( 2)
              gf
                      1 
                      2    g (f2 ) 
                                         
                                       Q ,T
                                        1   1   
                                    
                                                                     28
              Thermodynamics:
Competition between the N=0 and the N=1 phase



      F

                    T* 1
                           T1   T0



                                     T
          F0


               F1




                                                29
                  Temperature-field phase diagram




                                                                              ?



                                                                              ?

                                                                    ?



               Our model                               Experiments (Chung et al. 2000)


S. Haddad et al. Phys. Rev. Lett., 89, 087001 (2002)
S. Haddad et al. Phys. Rev B, 72, 085104 (2005)                                      30
    Effect of a parallel magnetic field

    c
                  H
         b                Free of
                          bird flu !


a                                      a

    Organic chains



                                           b


        Confinement in
        the (a,b) plane


                                               31
                                            Experiment (Danner et al. 1997)




           Our model


submitted to Eur. Phys. J. B




                               Joo et al. 2006                                32
Quantum mechanical calculation




            Layer index          33
Other models in competition with our !!!
Probability in transverse direction


                                      A. G. Lebed, Phys. Rev. Lett. (2005)




                       Index layer

                                                    But,
                                       does not explain the resistance
                                                  behavior




                                                                             34
                   What should be next ?


 symmetry of the gap in (TMTSF)2ClO4?    triplet or singlet ?

Interplay between Superconductivity and SDW : coexistence or
competition ?




          SDW

                                                 Sc




                                                                 35

				
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