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

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

The Theoretical Model

• A single zigzag chain:

Cu O

The Theoretical Model

• A single zigzag chain:

Cu O+

_

px

+_

py

++

--

d

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

Spin Gap from DMRG

0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

1/Length

s

ESz=1-ESz=0ESz=2-ESz=1

ESz=1

-ESz=0

ESz=2

-ESz=1

L=40N=50

L=32N=40

L=48N=60

L=80N=100