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The Three Hallmarks of Superconductivity Zero Resistance Complete Diamagnetism Macroscopic Quantum Effects Flux F V 0 Tc Temperature Magnetic Induction DC Resistance I T>Tc 0 T<Tc Tc Temperature 1 Flux quantization F = nF0 Josephson Effects Zero Resistance R = 0 only at w = 0 (DC) R > 0 for w > 0 E Quasiparticles 2D The Kamerlingh Onnes resistance measurement of mercury. At 4.15K the resistance suddenly dropped to zero Energy Gap 0 2 Cooper Pairs Perfect Diamagnetism Magnetic Fields and Superconductors are not generally compatible The Meissner Effect Superconductor H H B 0 H M 0 l(T) magnetic penetration depth l superconductor H H 0 e z / lL l 3 T<Tc Spontaneous exclusion of magnetic flux B0 z surface screening currents l(0) l is independent of frequency (w < 2D) H T>Tc H z vacuum H Tc T The Yamanashi MLX01 MagLev test vehicle achieved a speed of 343 mph (552 kph) on April 14, 1999 What are the Limits of Superconductivity? Phase Diagram Jc Normal State Superconducting State Tc Ginzburg-Landau free energy density 4 Temperature dependence Currents 0Hc2 Applied magnetic field BCS Theory of Superconductivity Bardeen-Cooper-Schrieffer (BCS) Cooper Pair s-wave ( = 0) pairing + + S + + Spin singlet pair v v + + + + S First electron polarizes the lattice Tc Debye e1/ NV Second electron is attracted to the concentration of positive charges left behind by the first electron Debye is the characteristic phonon (lattice vibration) frequency N is the electronic density of states at the Fermi Energy V is the attractive electron-electron interaction A many-electron quantum wavefunction Y made up of Cooper pairs is constructed with these properties: An energy 2D(T) is required to break a Cooper pair into two quasiparticles (roughly speaking) Cooper pair size: vF 5 D http://www.chemsoc.org/exemplarchem/entries/igrant/hightctheory_noflash.html Where do we find Superconductors? Also: Nb-Ti, Nb3Sn, A3C60, NbN, MgB2, Organic Salts ((TMTSF)2X, (BEDT-TTF)2X), Oxides (Cu-O, Bi-O, Ru-O,…), Heavy Fermion (UPt3, CeCu2Si2,…), Electric Field-Effect Superconductivity (C60, [CaCu2O3]4, plastic), … Most of these materials, and their compounds, display spin-singlet pairing 6 The High-Tc Cuprate Superconductors Layered structure – quasi-two-dimensional Anisotropic physical properties Ceramic materials (brittle, poor ductility, etc.) Oxygen content is critical for superconductivity YBa2Cu3O7-d Tl2Ba2CaCu2O8 Two of the most widely-used HTS materials in applications 7 Spin singlet pairing d-wave ( = 2) pairing