1. Superconductivity in Zigzag CuO Chains
Erez Berg, Steven A. Kivelson
Stanford University

2. 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

3. Introduction to Pr2 Ba4Cu7O15-
Structure: like the high Tc YBCO-247
CuO Plane
CuO Single Chain
Insulating and AF ordered!
Structure like YBCO with Tc=110K
However, transport properties are extremely different
CuO Planes: essential for SC in YBCO, insulating and AF in PrBaCuO
Single Chains
Double chains
Single crystal: very quasi 1d conductivity
Single chains are disordered, double chains are conducting
CuO Double Chain
For single crystals:
b/a1000

4. Superconductivity in Pr2 Ba4Cu7O15-
[1] M. Matsukawa et al., Physica C 411 (2004) 101–106
[2] S. Sasaki et al., cond-mat/
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
=0
Superconductivity discovered by Y. Yamada’s group in Japan
At delta=0, conductivity is metallic
When delta is increased, superconductivity appears with a maximal Tc of about 15K at delta=0.45
The same group presented evidence that it is the double chains that are responsible for superconductivity
They did Cu NQR, which is like NMR but you use the coupling of the Cu quadropole moments of the nuclei to local EFG instead of external magnetic fields
This way you can distinguish between inequivalent copper sites in the lattice
The found a sharp feature in 1/T1 vs T of the double chain coppers at Tc, but of no other copper site, which implies that that is where sc is occuring
Why this problem is interesting?
Because it’s a q1d superconductor, which we have chance to understand
Because the zigzag chain appears in other materials
=0.45
Tc15K

5. The Theoretical Model
A single zigzag chain: Cu O

6. The Theoretical Model
A single zigzag chain: + - d + _ py Cu O + _ px

7. Schematic Phase Diagram
Recent results:
Increasing 
=0
Coupling Constant, U
Phase seperation
Super- conducting
Q1D metal?
CDW?
1. This is a schematic phase diagram. Explain the axis
2. The physical initial state and path for delta>0
3. What do we mean by superconductivity in 1d?
4. Weak coupling limit
5. Results on strong coupling
Superconducting
Doping, n
“Half Filling”: one hole per copper

8. J2 is strongly frustrated!
Strong Coupling
Half Filling
The charge degrees of freedom are gapped
Effective spin interactions: J1 J2 Cu O
J1>0 (AF)
J2<0 (FM)
J2 is strongly frustrated!

9. Strong Coupling
Half Filling
For this system, the spin gap is exponentially small exp(-const.|J1/ J2|) J1 Cu O J2
Affleck and White (1996)
Itoi and Qin (2000)

10. 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

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

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

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

14. 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!

15. 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:

16. DMRG Simulation System of length=80 Cu sites with doping x=0.25
Open Boundary Conditions

17. DMRG Simulation System of length=80 Cu sites with doping x=0.25
Spin/Charge density profiles near the edge of the system:

18. 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

19. Spin Gap from DMRG