Superconductivity in Zigzag CuO Chains

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. CuO Plane CuO Single Chain CuO Double Chain Introduction to Pr2 Ba4Cu7O15- Structure: like the high Tc YBCO-247 Insulating and AF ordered! For single crystals: b/a1000

4. Superconductivity in Pr2 Ba4Cu7O15- [1] M. Matsukawa et al., Physica C 411 (2004) 101–106 [2] S. Sasakiet al., cond-mat/0603067 • 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 =0.45 Tc15K

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

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

7. Super-conducting Phase seperation Superconducting Schematic Phase Diagram Recent results: Increasing  =0 Coupling Constant, U Q1D metal? CDW? Doping, n “Half Filling”: one hole per copper

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

9. J1 J2 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)

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

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

13. Strong Coupling Finite Filling • Doping can relieve the frustration: 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 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:

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