W HAT IS S UPERCONDUCTIVITY? Basic expt: (Onnes 1911)

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W HAT IS S UPERCONDUCTIVITY? Basic expt: (Onnes 1911). V. Cu A l Cu. ~. S. S. perfect diamagnetism (Meissner effect) equilibrium effect. persistent currents, astronomically stable metastable effect.
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WHAT IS SUPERCONDUCTIVITY?Basic expt: (Onnes 1911)V Cu Al Cu~SSperfect diamagnetism(Meissner effect)equilibrium effectpersistent currents, astronomically stablemetastable effectNo a priori guarantee these two phenomena always go together!(but in fact seem to, in all “superconductors” known to date).z, supr.STRUCTURE OF A TYPICAL CUPRATEn = 1, 2, 3…(“homologous series”)“charge reservoir”“spacer”(alk. earth, rare-earth, Y, La….)Ex: (Tl –2212, n = 2)Cu++O– –~3.5Å~10ÅCa++Charge reservoir(Tl2Ba2O4)CuO2 plane as viewed from above:Note: Each CuO2 plane has valency—2e per formula unit, hence homologous series require spacer with +2e (i.e., typically alkaline earth (Ca++, Sr++ . . .)(Ca++)(Cu++)(O--)“CANONICAL” PHASE DIAGRAM OFCUPRATES AS FUNCTION OF T AND DOPING (COMPOSITE):“Strange metal”Pseudogap(UD)Tc(p)OD(“Fermi-Liquid”)AF insulatorT Superconductor0•160•27p Mott InsulatorIn-plane doping per CuO2 unit“optimal” doping(p 0•18(?))CuDoping: e.g. Y Ba2 Cu3 O6+x, La2–x Srx CuO4O For any given compound, can find mapping from x (chemical stoichiometry) to p(no. of holes per CuO2 unit in plane) which makes phase diagram and properties “per plane” approx. “universal,” : but difficult to check directly.: SOME BASIC FACTS ABOUT CUPRATES
  • Until 2008, unique in showing (reproducible) supy at T> 50 K. (>200 different materials). (2008: FeAs compounds, T~55K).
  • However,  some cuprates which can never be made superconducting (multilayers spaced by Sr or Ba).
  • Both N– and S– state props. highly anisotropic (e.g., in Bi 2212, c/ab ~105)
  • Many N-state props. very anomalous (e.g., ab ~T,H ~a + bT2). (S: rather “normal”!)
  • Most N- (and S-) state props. approximately consistent with hypothesis that at given doping, properties of CuO2 phase are universal. ( transport properties prob. sensitive to near-plane disorder, e.g. La2–xSrxCuO4.)
  • When S state occurs, v. sensitive to doping and pressure, (e.g., Hg–1201: Tc = 95 – 120 K)Atm. 20 GPa
  • For Ca-spaced homologous series, Tc always rises with layer multiplicity n up to n = 3, thereafter falls slightly. (?)
  • Macroscopic EM props of S state show large fluctuations, esp. in high magnetic fields (extremetype-II)
  • RT “Tc”WHAT DO WE KNOW FOR SURE ABOUTSUPERCONDUCTIVITY IN THE CUPRATES?
  • Flux quantization and Josephson experiments  ODLRO in 2-particle correlation function, i.e., superconductivity due to formation of Cooper pairs,
  • i.e.:
  • basic “topology” of many-body wave function is
  • ~A{(r1r212)(r3r434)….(rN–1rNN–1N)}
  • antisymmetricSame “molecular” wave function for all pairs (quasi-BEC!)For most purposes, more convenient to work in terms of related quantity“pair wave function” (anomalous average)Note: “Macroscopic wave function” of Ginzburg and Landau, (R), is just F(r1r212) for 1= –2=+1, r1 = r2 = R, i.e. wave function of COM of Cooper pairs.tripletsingletsTc and (b) Hc:WHAT DO WE KNOW FOR SURE . . . .? (cont.)
  • 6. Josephson (phase-sensitive) experiments  at least in YBCO, Tl-2201, NCCO. . . .symmetry of pair wave function is dx2–y2i.e. odd under /2 rotn in ab-plane,even under refln in a- or b-axis(in bulk: near (110) surface, d + is?)
  • c-axis resistivity  hopping time between unit cells along c-axis » /kBTpairs in different multilayers effectively independent(but cf. Anderson Interlayer Tunneling theory)
  • Absence of substantial isotope effect (in higher –Tc cuprates) + “folk-theorems” on Tcphonons do not play major role in cuprate superconductivity.( Newns and Tsuei)
  • NOTE: AT LEAST 95% OF LITERATURE MAKESALL OF ABOVE ASSUMPTIONS AND A LOT MOREe.g. 2d Hubbard, t-J, gauge field … all special cases of generic Hamiltonians based on these features.
  • + +––––+ +[: Li et al.]HOW WILL WE KNOW WHEN WE HAVE A “SATISFACTORY” THEORY OF HTS IN THE CUPRATES?Thesis: We should (at least) be able to: (A) give a blueprint for building a robust room-temperature superconductor,OR (B) assert with confidence that we will never be able to build a (cuprate-related) RT superconductorOR (C) say exactly why we cannot do either (A) or (B)In the meantime, a few more specific questions: (1) Are the cuprates unique in showing HTS? (2) If so, what is special about them? (e.g. band structure, 2-dimensionality, AF …) (3) Should we think of HTS as a consequence of the anomalous N-state properties, or vice versa? (4) Is there a second phase transition associated with the T* line? If so, what is the nature of the LT (“pseudogap”) phase? (5) If yes to (4), is this relevant to HTS or a completely unconnected phenomenon? (6) Why does Tc depend systematically on n in homologous series?SOME REPRESENTATIVE CLASSES OF “MODELS” OFCOOPER PAIRING IN THE CUPRATES(conservative exotic):
  • Phonon-induced attraction (“BCS mechanism”) problems: N-state ab(T)T down to T~10 K (Bi-2201 Tc)no isotope effect in higher –Tc HTSfolk-theorems on Tc (but : FeAs compounds)
  • Attraction induced by exchange of some other boson:— spin fluctuations— excitons— fluctuations of “stripes”— more exotic objects
  • Theories starting from single-band Hubbard model:*
  • Attempts at direct solution, computational or analytic
  • Theories based on postulate of “exotic ordering” in groundstate (e.g. spin-charge separation)
  • Problems: — to date, no direct evidence for exotic order
  • — T* line appears to be unrelated to Tc
  • (and, “Nature has no duty ….”)
  • ↑ ↑ hopping on-site repulsion*See e.g. P.A. Lee, Reps. Prog. Phys. 71, 012501 (2008)()potential en of cond.n e-,s in field of static latticeIHOW CAN PAIRING SAVE COULOMB ENERGY?[exact]bare densityresponse functionCoulomb interaction(repulsive)A. (typical for )pertn-theoretic result
  • to decrease must decrease
  • but  gap should change sign (d-wave?)B. (typical for )
  • to decrease (may) increase
  • and thus (possibly) increased correlations  increased screening  decrease of Coulomb energy! electrons haveopposite momentum (and spin)electrons havearbitrary momentum (and spin)ELIASHBERG vs. OVERSCREENING–k' interactionfixedk'ELIASHBERGk–k REQUIRES ATTRACTION IN NORMAL PHASEinteraction modified by pairingk3k4OVERSCREENINGk1k2NO ATTRACTION REQUIRED IN NORMAL PHASE
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