1. High Temperature Superconductivity: D. Orgad Racah Institute, Hebrew University, Jerusalem Stripes: What are they and why do they occur Basic facts concerning the cuprates Experimental signatures of stripes Consequences of stripe formation: Fractionalization Confinement Outline: Are stripes good or bad for superconductivity ? S. Kivelson V. Emery E. Carlson M. Granath V. Oganesyan X-J. Zhou Z-X. Shen Z-X. Shen

2. The Cuprates: Basic Structure Universal element – CuO planes Parent (undoped) compounds – Heisenberg antiferromagnets Hole doping by chemical substitution / Oxygen doping

3. The Cuprates: Typical Phase Diagram x T SC AF underoptimalover doping The Central Question: What happens to an AF upon doping with holes ? UD Bi2212 tunneling ARPES NMR DC resistivity Optical conductivity Pseudogap Neutron scattering, Specific heat … Renner et al.Harris et al.Warren et al. Puchkov et al. Takagi et al.

4. Holes in an AF : Why Do Stripes Occur? PHASE SEPARATION Coulomb Interactions Kinetic Energy Frustration STRIPES

5. Stripes in Other Systems: Competing Interactions Ferrofluid between glass platesFerromagnetic garnet film Block copolymers film  cm  m 

6. Stripe Signatures in S(k,  Real Space Momentum Space kyky kxkx kyky kxkx

7. Experimental Evidence for Stripes: Neutron Scattering Static stripe order (LNSCO) kyky kxkx Dynamic stripes (YBCO) Mook et al. E=24.5meV Tranquada et al. 0.25 0.12

8. Experimental Evidence for Stripes: ARPES Angle Resolved PhotoEmission Spectroscopy measures the single hole spectral functionLNSCO

9. Experimental Evidence for Stripes: Tunneling Microscopy Hoffman et al. Howald et al. B=5T B=0

10. Consequences of Stripe Formation: Spin-gap and Enhanced SC Correlations StripesDoped Spin Ladders: known to be spin-gapped SC x PG AF T The spin-gap creates an amplitude of the SC order parameter Provides high pairing scale (avoid Coulomb repulsion)

11. A Problem … In 1D a spin-gap enhances pairing: Good News: divergent for K c >1/2 (K c <1 for repulsive interactions) Bad News: It also enhances CDW correlations: more divergent ! Old problem from search for organic superconductors

12. L1L1 L2L2 y x y2y2 y1y1 Stripe fluctuations dephase CDW coupling: Stripe fluctuations enhance phase coupling: SC PG x T Phase Stiffness staticfluctuatingdissolved Nematic? Stripe fluctuations (quantum, thermal or quenched) are necessary for high T c ! Phase Stiffness AF Yamada et al. … And Its Resolution

13. Consequences of Stripe Formation: Electron Fractionalization Above T c In a Fermi liquid the elementary excitations have the quantum numbers of an electron Valla et al. Mo surface state qp peak multi-qp background In a Luttinger liquid the excitations come in 4 flavors MDC EDC MDC EDC

14. Evidence for Fractionalization Sharp in MomentumBroad in Energy 1DEG Orgad et al. ARPES in La 1.25 Nd 0.6 Sr 0.15 CuO 4 Breakdown of W-F Law in Pr 1.85 Ce 0.15 CuO 4 Hill et al.

15. Below T c : A Coherent Peak Optimally Doped BSCCO (T c =91K) Not a Conventional QP Not present above T c Intensity grows below T c Energy and lifetime not temperature dependent Fedorov et al.

16. Josephson Coupling Confines 1D Solitons The electronic operatorcreates kinks in and Frustrated Josephson Coupling between solitons Bound spin-charge soliton pair Charge and spin solitons createphase shift in pair field s c

17. A < (k  in the Superconducting Phase incoherent Quasiparticle weight depends on superfluid density: Feng et al.

18. Conclusions Stripes are ubiquitous in the cuprate high temperature superconductors superconductors They are important for high temperature superconductivity superconductivity There is evidence that the normal state of the cuprates is fractionalized is fractionalized In a quasi-one-dimensional superconductor T c also marks a confinement transition marks a confinement transition

19. Landau Theory of Stripe Phases Coupled charge (CDW) order and spin (SDW) order Stripes are “charge driven” : Spin order is secondary and may be absent Zachar et al.

20. Spin-gap Proximity Effect Single particle tunneling irrelevant Pair tunneling possible “system”“environment” tunneling is relevant. When The spin modes and the relative charge phase mode are gapped. The only gapless mode involves the total SC phase Kinetic energy driven pairing Repulsive interactions within system and environment increase  Repulsive interactions between system and environment decrease  Pre-existing spin-gap in environment decreases 

21. ARPES and Stripes Angle Resolved PhotoEmission Spectroscopy measures the single hole spectral function LNSCO Zhou et al.LNSCOLSCO

22. Disordered Stripe Array: Spectral Weight Granath et al. Low Energy Spectral Weight

23. Disordered Stripe Array: Interacting Spectral Function Granath et al.

24. A Model: Quasi-one-dimensional Superconductor Charge: Gapless Spin: Gapped Weak Pair Tunneling (Couples charge and spin)

25. Prediction: New Magnetic Resonance Neutron scattering measures the spin-spin correlation function: creates 2 spin solitons and 2 charge solitons Treat more massive spin solitons as static and solve for the charges: ss Get effective Schrodinger equation for spins: Spin 1 mode that exists below 0.4 T c 2k F mode: should appear around Threshold at 2  s