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• 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
CuO Plane
CuO Single Chain
CuO Double Chain
Insulating and AF ordered!
Introduction to Pr2 Ba4Cu7O15-
Structure: like the high Tc YBCO-247
For single crystals:
b/a1000
Superconductivity in Pr2 Ba4Cu7O15-
=0
=0.45
• Upon oxygen reduction (>0), the material becomes superconducting at low T [1]
• An NQR experiment [2] shows evidence that the superconductivity occurs in the double chains
[1] M. Matsukawa et al., Physica C 411 (2004) 101–106
[2] S. Sasaki et al., cond-mat/0603067
Tc15K
Schematic Phase Diagram
Coupling Constant, U
“Half Filling”: one hole per copper
Doping, n
Superconducting0U
=0Increasing
Super-conducting
Q1D metal?
CDW?
Phase seperation
Recent results:
Strong CouplingHalf Filling
• The charge degrees of freedom are gapped
• Effective spin interactions:
Cu O
J1>0 (AF)
J2<0 (FM)
J1
J2
J2 is strongly frustrated!
Strong CouplingHalf 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 CouplingFinite Filling
Cu O
• 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
Strong CouplingFinite Filling
• Doping can relieve the frustration:
Relieving of the frustration is maximal if neighboring doped holes go into opposite chains!
Strong CouplingFinite Filling
• Doping can relieve the frustration:
Relieving of the frustration is maximal if neighboring doped holes go into opposite chains!
Strong CouplingFinite Filling
• Doping can relieve the frustration:
Relieving of the frustration is maximal if neighboring doped holes go into opposite chains!
Strong CouplingFinite 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 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:
The “alternating phase” is good for superconductivity:
DMRG SimulationSystem of length=80 Cu sites
with doping x=0.25Open Boundary Conditions
0 20 40 60 800.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
position
Oxy
ge
n h
ole
de
nsi
ty
Chain 1Chain 2
DMRG SimulationSystem 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