Outline: • Basic facts concerning the cuprates • Stripes: What are they and why do they occur • Experimental signatures of stripes • Are stripes good or bad for superconductivity ? • Consequences of stripe formation: • Fractionalization • Confinement High Temperature Superconductivity: S. Kivelson V. Emery E. Carlson M. Granath V. Oganesyan X-J. Zhou Z-X. Shen D. Orgad Racah Institute, Hebrew University, Jerusalem
The Cuprates: Basic Structure • Universal element – CuO planes • Parent (undoped) compounds – Heisenberg antiferromagnets • Hole doping by chemical substitution / Oxygen doping
Renner et al. Harris et al. Warren et al. Takagi et al. T tunneling UD Bi2212 Puchkov et al. NMR ARPES Pseudogap AF SC DC resistivity x under optimal over Neutron scattering, Specific heat … doping Optical conductivity The Central Question: What happens to an AF upon doping with holes? The Cuprates: Typical Phase Diagram
Holes in an AF : Why Do Stripes Occur? Coulomb Interactions PHASE SEPARATION STRIPES Kinetic Energy Frustration
Stripes in Other Systems: Competing Interactions Ferrofluid between glass plates Ferromagnetic garnet film l~1cm l~10mm l~10mm l~400A Ferromagnetic garnet film Block copolymers film
ky kx ky kx Stripe Signatures in S(k,w) Real Space Momentum Space
Experimental Evidence for Stripes: Neutron Scattering ky Static stripe order (LNSCO) kx 0.25 E=24.5meV Dynamic stripes (YBCO) 0.12 Mook et al. Tranquada et al.
LNSCO Experimental Evidence for Stripes: ARPES Angle Resolved PhotoEmission Spectroscopy measures the single hole spectral function
Experimental Evidence for Stripes: Tunneling Microscopy B=5T B=0 Howald et al. Hoffman et al.
The spin-gap creates an amplitude of the SC order parameter • Provides high pairing scale (avoid Coulomb repulsion) Consequences of Stripe Formation: Spin-gap and Enhanced SC Correlations Stripes Doped Spin Ladders: known to be spin-gapped T PG AF SC x
Bad News: It also enhances CDW correlations: more divergent ! Old problem from search for organic superconductors A Problem … Good News: In 1D a spin-gap enhances pairing: divergent for Kc>1/2 (Kc<1 for repulsive interactions)
T Stripe fluctuations (quantum, thermal or quenched) are necessary for high Tc! y2 y1 Nematic? Phase Stiffness L1 L2 Phase Stiffness PG AF SC Yamada et al. x static fluctuating dissolved x y … And Its Resolution Stripe fluctuations dephase CDW coupling: Stripe fluctuations enhance phase coupling:
In a Fermi liquid the elementary excitations have the quantum numbers of an electron Mo surface state multi-qp background Valla et al. qp peak In a Luttinger liquid the excitations come in 4 flavors MDC EDC EDC MDC Consequences of Stripe Formation:Electron Fractionalization Above Tc
ARPES in La1.25Nd0.6Sr0.15CuO4 Breakdown of W-F Law 1DEG in Pr1.85Ce0.15CuO4 Orgad et al. Hill et al. Sharp in Momentum Broad in Energy Evidence for Fractionalization
Not a Conventional QP • Not present above Tc • Intensity grows below Tc • Energy and lifetime not • temperature dependent Below Tc: A Coherent Peak Optimally Doped BSCCO (Tc=91K) Fedorov et al.
and Charge and spin solitons create phase shift in pair field s c Frustrated Josephson Coupling between solitons Bound spin-charge soliton pair Josephson Coupling Confines 1D Solitons The electronic operator creates kinks in
Feng et al. A<(k,w) in the Superconducting Phase incoherent • Quasiparticle weight depends on superfluid density:
Conclusions • Stripes are ubiquitous in the cuprate high temperature • superconductors • They are important for high temperature • superconductivity • There is evidence that the normal state of the cuprates • is fractionalized • In a quasi-one-dimensional superconductor Tc also • marks a confinement transition
Stripes are “charge driven” : Spin order is secondary and may be absent Landau Theory of Stripe Phases Coupled charge (CDW) order and spin (SDW) order Zachar et al.
“system” “environment” tunneling is relevant. Spin-gap Proximity Effect Single particle tunneling irrelevant possible Pair tunneling 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 a • Repulsive interactions between system and environment decrease a • Pre-existing spin-gap in environment decreases a
LNSCO LSCO Zhou et al. ARPES and Stripes Angle Resolved PhotoEmission Spectroscopy measures the single hole spectral function LNSCO
Disordered Stripe Array: Spectral Weight Low Energy Spectral Weight Granath et al.
Disordered Stripe Array: Interacting Spectral Function Granath et al.
Weak Pair Tunneling (Couples charge and spin) A Model:Quasi-one-dimensional Superconductor Charge: Gapless Spin: Gapped
Spin 1 mode that exists below 0.4 Tc • 2kF mode: should appear around • Threshold at 2Ds 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: s s Get effective Schrodinger equation for spins: