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
d
-
• A single zigzag chain:
+
+
py O
_
+
px
_
Cu
-
+
Schematic Phase Diagram
Recent results:
Increasing 
Coupling
Constant, U
Superconducting
=0
Q1D metal?
CDW?
Phase
seperation
Superconducting
U 0
“Half Filling”:
one hole per copper
Doping, n
Strong Coupling
Half Filling
• The charge degrees of freedom are gapped
• Effective spin interactions:
Cu
J1
O
J2
J1>0 (AF)
J2<0 (FM)
J2 is strongly
frustrated!
Strong Coupling
Half Filling
• For this system, the spin gap is
exponentially small exp(-const.|J1/ J2|)
Cu
J1
O
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
Oxygen hole density
0.32
0.3
0.28
0.26
0.24
0.22
0.2
Chain 1
Chain 2
0
20
40
position
60
80
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
E -ESz=0-E
ESz=2Sz=1
-ESz=1
Sz=0
ESz=2-ESz=1
0.04
L=32
N=40
0.035
s
0.03
L=48
N=60
0.025
0.02
L=80
N=100
0.015
0.01
L=40
N=50
0.005
0
0
0.005
0.01
0.015
0.02
1/Length
0.025
0.03
0.035