Superconductivity in Zigzag CuO Chains

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Superconductivity in Zigzag CuO Chains

• Erez Berg, Steven A. Kivelson
• Stanford University

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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

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Introduction to Pr2 Ba4Cu7O15-?
Structure like the high Tc YBCO-247
Insulating and AF ordered!
For single crystals ?b/?a?1000
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Superconductivity in Pr2 Ba4Cu7O15-?
1 M. Matsukawa et al., Physica C 411 (2004)
101106 2 S. Sasaki et al., cond-mat/0603067

• Upon oxygen reduction (?gt0), the material
  becomes superconducting at low T 1
• An NQR experiment 2 shows evidence that the
  superconductivity occurs in the double chains

?0
?0.45
Tc?15K
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The Theoretical Model

• A single zigzag chain

Cu
O
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The Theoretical Model

• A single zigzag chain

Cu
O
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Schematic Phase Diagram
Recent results
Increasing ?
?0
Coupling Constant, U
Q1D metal? CDW?
Doping, n
Half Filling one hole per copper
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Strong Coupling
Half Filling

• The charge degrees of freedom are gapped
• Effective spin interactions

Cu
O
J1gt0 (AF) J2lt0 (FM)
J2 is strongly frustrated!
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Strong Coupling
Half Filling

• For this system, the spin gap is exponentially
  small ??exp(-const.J1/ J2)

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

• Doping can relieve the frustration

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

• Doping can relieve the frustration

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

• Doping can relieve the frustration

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

• Minimum magnetic energy configuration holes
  appear in alternating order in the two chains
• Magnetic energy gained Em/L? ?s2 ?J22x2 (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!
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Relation to Superconductivity?
The alternating phase is good for
superconductivity

• The relative charge mode ?-,c is gappedwith ?-,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

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DMRG Simulation
System of length80 Cu sites with doping
x0.25 Open Boundary Conditions
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DMRG Simulation
System of length80 Cu sites with doping x0.25
Spin/Charge density profiles near the edge of the
system
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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

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Spin Gap from DMRG