3 500 referencesV. J. Emery, S. A. Kivelson, E.Arrigoni, I.Bindloss, E.Carlson, S.Chakravarty, L.Chayes, K.Fabricius, E.Fradkin, M.Granath, D-H.Lee, H-Q. Lin, U.Low, T.Lubensky, E.Manousakis, Z.Nussinov, V.Oganesyan, D.Orgad, L.Pryadko, M.Salkola, Z-X.Shen, J.Tranquada, O.Zachar
4 Superconductivity Fermions: Pauli exclusion principle Bosons can condenseStable phase of matterMacroscopic Quantum BehaviorPair wavefunction acts like “order parameter”
5 Superconductivity Fermions: Pauli exclusion principle Bosons can condenseStable phase of matterMacroscopic Quantum BehaviorPair wavefunction acts like “order parameter”
6 Conventional Superconductivity John BardeenLeon CooperBob SchriefferConventional SuperconductivityBCS TheoryInstability of the metallic state
7 Simple Metals: The Fermi Gas Fermi SurfaceFree Electrons E ~ k2Pauli exclusion principleFill to Fermi levelAdiabatically turn on temperature, most states unaffectedVery dilute gas of excitations: quasiparticlesKE most importantPauli exclusion principlefill to Fermi levelFermi seaStable except for …
8 Simple Metals: The Fermi Liquid Fermi SurfacePauli exclusion principleFill to Fermi levelAdiabatically turn on temperature, most states unaffectedVery dilute gas of excitations: quasiparticlesFermi Gas + Interactions Fermi LiquidKinetic EnergyDominantQuasiparticles = Dressed Electrons
9 Retardation is Essential Cooper PairingFermi Liquid Unstable to PairingPair electrons near Fermi SurfacePhonon mediatedRetardation is Essentialto overcomeCoulomb repulsion
10 Of A Tranquil Fermi Sea— BCS Haiku:InstabilityOf A Tranquil Fermi Sea—Broken Symmetry
11 High Temperature Superconductors HgCuOYBCO7LSCO
12 High Temperature Superconductors Copper Oxygen PlanesOther LayersLayered structure quasi-2D systemLayered structure quasi-2D system
13 High Temperature Superconductors Copper-Oxygen Planes Important“Undoped” is half-filledAntiferromagnetNaive band theory failsStrongly correlatedOxygenCopper
14 High Temperature Superconductors Dope with holesSuperconducts at certain dopingsTAFSCxOxygenCopper
15 Mysteries of High Temperature Superconductivity Ceramic! (Brittle)“Non-Fermi liquid” normal stateMagnetism nearby (antiferromagnetism)Make your own (robust)PseudogapPhase ordering transition
16 Two Energy Scales in a Superconductor Two component order parameterAmplitudePairingGapPhasePhase CoherenceSuperfluid Density
17 BCS is a mean field theory in which pairing precipitates order 4238Y-123 (ud)62104Bi-2212 (od)14090116Y-123 (op)55Y-123 (od)6095220Bi-2212 (op)83275Bi-2212 (ud)2526Tl-2201 (od)1608091122Tl-2201 (op)130133435Hg-1223 (op)108290Hg-1212 (op)18096192Hg-1201 (op)10020LSCO (od)5458LSCO (op)473075LSCO (ud)MaterialPhase FluctuationsImportant in CupratesEmery, Kivelson, Nature, 374, 434 (1995)EC, Kivelson, Emery, Manousakis, PRL 83, 612 (1999)MaterialPb7.97.26X105Nb3Sn18.717.82X104UBe130.80.9102BaKBiO17.4265X102K3C602620102MgB215391.4X103
18 Tc and the Energy Scales superconductivityAFxBCS: ~ 1000 TcHTSC: ~ Tc underdoped
19 Mysteries of High Temperature Superconductivity Ceramic! (Brittle)“Non-Fermi liquid” normal stateMagnetism nearby (antiferromagnetism)Make your own (robust)PseudogapPhase ordering transitionBCS to the rescue?
20 There is no room for retardation in the cuprates BCS:Cuprates:How do we get a high pairing scaledespite the strong Coulomb repulsion?
21 A Fermi Surface Instability Requires a Fermi Surface! How do we get superconductivityfrom a non-Fermi liquid?
22 Strong Correlation Fermi Liquid k-space structure Kinetic energy is minimizedPairing is potential energy drivenReal space structureKinetic energy is highly frustratedSystem works to relieve KE frustration
23 Doped Antiferromagnets Hole Motion is Frustrated
24 Doped Antiferromagnets Compromise # 1: Phase SeparationRelieves some KE frustrationPureAFHoleRichLike Salt Crystallizing From Salt Water,The Precipitate (AF) is Pure
25 Coulomb Frustrated Phase Separation Long range homogeneityShort range phase separationCompromise # 2: mesoscale structurePatches interleavequasi-1D structure – stripes ?HoleRichPoor
26 Stripes Rivers of charge between antiferromagnetic strips Electronic structure becomes effectively 1D
27 Competition often produces stripes Ferromagnetic garnet filmFaraday effectPeriod ~ mFerrofluid confined between two glass platesPeriod ~ 1cmFerromagnetic garnet filmPeriod ~ mBlock copolymersPeriod ~ 4X10-8 m
28 What’s so special about 1D? canalJohn Scott Russell's Soliton Wave Re-createdOn Wednesday 12 July 1995, an international gathering of scientists witnessed a re-creation of the famous 1834 'first' sighting of a soliton or solitary wave on the Union Canal near Edinburgh. They were attending a conference on nonlinear waves in physics and biology at Heriot-Watt University, near the canal. The occasion was part of a ceremony to name a new aqueduct after John Scott Russell, the Scottish scientist who made the original observation. The aqueduct carries the Union Canal over the Edinburgh City Bypass.In 1834, John Scott Russell was observing a boat being drawn along 'rapidly' by a pair of horses. When the boat suddenly stopped Scott Russell noticed that the bow wave continued forward "at great velocity, assuming the form of a large solitary elevation, a well-defined heap of water which continued its course along the channel apparently without change of form or diminution of speed". Intrigued, the young scientist followed the wave on horseback as it rolled on at about eight or nine miles an hour, but after a chase of one or two miles he lost it.What’s so special about 1D?
29 1D: Spin-Charge Separation spin excitationcharge excitationpoint out topological, 1D special, point-like, and higher D different.
30 1D: “Bosonization transformation” Expresses fermions as kinks in boson fields:spin solitonelectron=+charge solitonHamiltonian of interacting fermionsbecomes Hamiltonian of non-interacting bosonsSpin Charge SeparationElectron No Longer Exists!Non-Fermi Liquid(Luttinger Liquid)
31 Advantages of a quasi-1D Superconductor non-Fermi liquidstrongly correlatedcontrolled calculations
32 Kinetic Energy Driven Pairing? Proximity EffectsuperconductormetalIndividually, free energies minimizedMetal pairs (at a cost!) to minimize kinetic energy across the barrier
34 Spin Gap Proximity Effect Kinetic energy driven pairing in a quasi-1D superconductorMetallic charge stripe acquires spin gap throughcommunication with gapped environment
35 Spin Gap Proximity Effect Kinetic energy driven pairing in a quasi-1D superconductorkF = k’FConserve momentum and energySingle particle tunneling is irrelevantkFk’F
36 Spin Gap Proximity Effect Kinetic energy driven pairing in a quasi-1D superconductorkF = k’FConserve momentum and energySingle particle tunneling is irrelevantBut pairs of zero total momentumcan tunnel at low energy pairs form to reduce kinetic energyStep 1: PairingkFk’F
37 1D is Special Spin Gap = CDW Gap = Superconducting Gap Which will win? CDW stronger for repulsive interactions (Kc<1)Don’t Make a High Temperature Insulator!
39 Inherent Competition think local stripe order superconductivityTJosephsoncouplingPairing think local stripe order think “stripe phonon”stripefluctuationsStatic StripesGood pairingBad phase coherenceFluctuating StripesBad pairingGood phase coherence
40 Behavior of a Quasi-1D Superconductor Treat rivers of charge as 1D objects
41 Behavior of a Quasi-1D Superconductor High Temperature Effective Dimension = 1Spin charge separation on the Rivers of ChargeElectron dissolvesNon-Fermi Liquid (Luttinger Liquid)Intermediate Temperature Effective Dimension = 1Rivers of charge acquire spin gap from local environmentPseudogapNon-Fermi Liquid (Luther-Emery Liquid)Low Temperature Effective Dimension = 31D system cannot order Dimensional CrossoverPair tunneling between rivers produces phase coherenceElectron recombines
42 Dimensional Crossover and the Quasiparticle Chains coupled in superconducting statec o n f i n e m e n tsceSuperconducting order parameter switches sign across each soliton
43 Dimensional Crossover and the Quasiparticle c o n f i n e m e n tscBound state of spin and charge Electron is stable in superconducting state
44 Crossover Diagram of a Quasi-1D Superconductor Do/21D Luttinger Liquid1D Luther-EmeryLiquid3D FermiLiquidTPseudogap3D SuperconductorGapt (increases with x?)Crossover Diagram of a Quasi-1D Superconductor
45 Is mesoscale structure necessary for high Tc superconductivity? Mesoscale structure can enhance pairing (spin-gap)May be necessary to get pairing from repulsionAlways bad for phase ordering
46 Conclusions Strongly correlated Kinetic Energy driven order Formation of mesoscale structureFormation of pairs by proximity effectPhase coherence by pair tunneling between stripesQuasi-1D Superconductor(Controlled calculations)Non-Fermi liquid normal statePseudogap stateStrong pairing from repulsive interactionsInherent competition between stripes and superconductivityDimensional crossover to superconducting stateStrong correlation leads to all sorts of new physics.I focused on 3 that can occur.“Controlled” is anthropomorphic