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Superconductivity in 1D

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					Superconductivity in
Zigzag CuO Chains

Erez Berg, Steven A. Kivelson
     Stanford University
                 Outline

• Pr2Ba4Cu7O15-: A new superconductor
• Evidence for quasi 1D superconductivity
• The theoretical model
• Phase diagram: from weak to strong coupling
• A possible mechanism of superconductivity:
  results from bosonizations and numerics
  (DMRG)
• Conclusions
Introduction to Pr2 Ba4Cu7O15-
      Structure: like the high Tc YBCO-247

                  CuO Plane

            CuO Single Chain
Insulating and AF
ordered!


         CuO Double Chain

   For single crystals:
   b/a1000
Superconductivity in Pr2 Ba4Cu7O15-
         [1] M. Matsukawa et al., Physica C 411 (2004) 101–
         106
         [2] S. Sasaki et al., cond-mat/0603067

• Upon oxygen reduction
(>0), the material becomes
superconducting at low T [1]             =0
• An NQR experiment [2]
shows evidence that the
superconductivity occurs in
the double chains
                                            =0.45

                                    Tc15K
      The Theoretical Model
• A single zigzag chain:


              Cu     O
      The Theoretical Model
• A single zigzag chain:
                             d




                                 -
                             +       +

                   py O




                                 -
              Cu



                    +
                    _
                         +

                    px

                    _
            Schematic Phase Diagram
                        Recent results:
                         Increasing             =0
 Coupling
 Constant, U
                          Super-        Q1D metal?
                        conducting        CDW?
                   Phase
                 seperation


                               Superconducting
                                                 U 0

                                                 Doping, n
  “Half Filling”:
one hole per copper
           Strong Coupling
                Half Filling

• The charge degrees of freedom are gapped
• Effective spin interactions:
      Cu   O        J1

               J2




                J1>0 (AF)      J2 is strongly
                J2<0 (FM)       frustrated!
            Strong Coupling
                     Half Filling

• For this system, the spin gap is
  exponentially small exp(-const.|J1/ J2|)
       Cu   O            J1

                    J2


                Affleck and White (1996)
                  Itoi and Qin (2000)
           Strong Coupling
                Finite Filling

• Doped holes are expected to go mostly into
  the oxygen orbitals
• A doped hole causes a  shift in the phase
  of AF fluctuations in its chain
              Cu   O
               Strong Coupling
                      Finite Filling
• Doping can relieve the frustration:




Relieving of the frustration is maximal if neighboring doped
                holes go into opposite chains!
               Strong Coupling
                      Finite Filling
• Doping can relieve the frustration:




Relieving of the frustration is maximal if neighboring doped
                holes go into opposite chains!
               Strong Coupling
                      Finite Filling
• Doping can relieve the frustration:




Relieving of the frustration is maximal if neighboring doped
                holes go into opposite chains!
               Strong Coupling
                     Finite Filling




• Minimum magnetic energy configuration: holes appear
  in alternating order in the two chains
• Magnetic energy gained: Em/L – s2 –|J2|2x2 (x is the
  doping)
• Kinetic energy cost of alternating order:
  Ek/L x3
     The magnetic part wins for small x
     At low enough x, the system phase seperates!
    Relation to Superconductivity?
The “alternating phase” is good for superconductivity:

• The relative charge mode -,c is gapped
  with -,c x Enhanced pairing correlations
• The residual long-range interactions between
  doped holes are attractive
• Superconductivity occurs At low doping, where
  the charge Luttinger exponent
  K+,c uc becomes large:
                       DMRG Simulation
                       System of length=80 Cu sites
                            with doping x=0.25
                       Open Boundary Conditions
                      0.34

                      0.32
Oxygen hole density




                       0.3

                      0.28

                      0.26

                      0.24

                      0.22                            Chain 1
                                                      Chain 2
                       0.2
                             0   20     40       60             80
                                      position
DMRG Simulation
System of length=80 Cu sites
     with doping x=0.25

Spin/Charge density profiles
near the edge of the system:
                  Conclusions
• In the new superconductor Pr2Ba4Cu7O15- there is
  evidence that superconductivity occurs in quasi-d
  zigzag CuO chains
• A model for a single zigzag CuO chain was studied by
  bosonization and DMRG
• From this model, we propose a possible mechanism of
  superconductivity
• Superconductivity is expected in a narrow region of
  doping near half filling
            Spin Gap from DMRG
    0.045       ESz=1-ESz=0
                   E      -E
                ESz=2Sz=1
                     -ESz=1    Sz=0
     0.04          ESz=2-ESz=1
                                                              L=32
    0.035                                                     N=40

     0.03
                                              L=48
    0.025                                     N=60
s





     0.02

    0.015
                              L=80
                              N=100
     0.01
                                                     L=40
                                                     N=50
    0.005

       0
            0    0.005    0.01        0.015   0.02   0.025   0.03    0.035
                                      1/Length

				
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posted:5/17/2012
language:English
pages:19