In General > s.a. types of superconductors; Models in Physics.
* Idea: A macroscopic quantum phenomenon, consisting in the abrupt and complete disappearance of the resistivity of certain materials when cooled below some critical temperature (typically, a few K).
* Reason: Superconductivity requires a "pairing interaction", an indirect attractive force between conduction electrons that can overcome their direct Coulomb repulsion, so that pairs of electrons can condense into a macroscopically coherent quantum state which manifests itself as a resistanceless fluid—a non-perturbative effect; In conventional low-temperature (BCS) superconductors lattice distortions provide the pairing interaction, leading to Bose condensation of Cooper pairs.
* History: 1911, Discovery by Heike Kamerlingh Onnes in Leiden; 1935, F&H London phenomenological model, containing a field penetration depth λ; 1950, Landau-Ginzburg model; 1953, Pippard's coherence length ξ0, measuring non-locality of the superconducting electrons; 1954, Sound attenuation by electron-phonon interaction measured; 1957, Bardeen, Cooper & Schrieffer's microscopic theory in terms of Cooper pairs; Abrikosov's theory; 1959, L Gorkov showed how the Landau-Ginzburg model follows from the BCS theory; 1962, Prediction of the Josephson effect; 1987, discovery of high-temperature superconductivity (90 K, higher than liquid He); 2005, High-T superconductivity still not understood, and even in conventional superconductors, Tao effect cannot be explained by BCS theory.
@ General references: Wreszinski a1506-conf [rev]; Malik 16 [approach based on the Bethe-Salpeter equation in the mean-field approximation].
@ History: Sauer AHES(07)phy/06 [and Einstein, 1919-1922]; Barsan & Ciobanu a0910 [two-band theory]; van Delft & Kes PT(10)sep; Wysokiński PF-a1109, a1111; Ranninger a1207 [and conceptual heritage]; Kadanoff JSP(13)-a1303 [Lev Landau and John Bardeen, and the importance of the condensate].

Conventional Superconductors, BCS Theory > s.a. phase transitions; types of superconductors.
* Landau-Ginzburg model: A phenomenological model for superconductivity, based on a macroscopic wavefunction ψ, with a dimensionless parameter κ; This defines the Ginzburg-Landau coherence length ξ:= λ/κ; > s.a. Wikipedia page.
* BCS theory: The phonon-electron coupling, at a critical Tc, produces a superconducting state with the right values of Δ, coherence length ξ, penetration depth λ, and critical field Hc; free electrons with opposite spins and, in the absence of applied currents or magnetic fields, equal and opposite momenta, form bound Cooper pairs that condense into a single macroscopic state described by

ψ(r, t) = |ψ(r, t)| exp{i φ(r, t)} ;

the phase φ is coherent throughout the superconductor; They are the basis of the BCS theory.
* Abrikosov: In type II superconductors, for k > \(\sqrt2\), a field H > Hc1 would penetrate in the form of tubes of quantized flux, but the material would remain superconducting up to H = Hc2.
@ General references: Feynman RMP(57); Bardeen, Cooper & Schrieffer PR(57), PR(57); Cooper AJP(59)feb; Bogoliubov ed-62 [reprints]; Balian et al PRP(99) [extension]; Rubinstein & Sternberg JMP(05) & issue [Ginzburg-Landau model]; Butch et al AJP(08)feb [RL]; Cooper & Feldman ed-10; Schmalian in(10)-a1008 [history, failed attempts]; news PhysOrg(11)jun [third mechanism for superconductivity identified]; Sigal a1308, Frank & Lemm AHP(16)-a1504 [Ginzburg-Landau model].
@ Books: London 61, 64; Blatt 64; Kuper 68; Tinkham 75; Vidali 93 [I]; Kopnin 01 [non-equilibrium]; Shrivastava 00; Ginzburg & Andryushin 04; Annett 04 [intro]; Poole et al 07; Blundell 09 [I].
@ Related topics: Hirsch PLA(03) [and Lorentz force]; Pan JMP(03) [near critical T]; Brandão NJP(05) [order parameter and entanglement]; Hirsch PLA(09) [new basis set to describe electrons]; Wilczek MPLA(10) [BCS theory and its effects on theoretical physics]; Sanayei et al a1807 [trimer states]; Magnen & Unterberger a1902 [derivation of T = 0 2D superconductivity]; > s.a. Density Functional Theory.

Properties, Effects > s.a. electricity [London's equations]; Josephson Effect; locality; symmetry breaking.
* And magnetic fields: The presence of an H above some Hc< 1 kG destroys the superconducting properties of the "soft" superconductors (Pb, Sn, ...); Explained by Walther Meißner (or Meissner) and Robert Ochsenfeld [@ Naturwiss(33)].
* Meißner effect: The effect by which superconductors exclude magnetic fields, observed by Huebener & Clem [@ RMP(74)]; Superconductors are perfect diamagnetic substances.
* Isotope effect: For many superconductors, Tc scales with isotopic mass as M−1/2, suggesting that phonons participate in the phenomenon.
* Specific heat: There is an exponential c, suggesting an energy gap D in the electronic excitation spectrum.
* Quantum phase slip: A quantum fluctuation in which the superconducting wavefunction spontaneously tunnels from one state into another; This results in a momentary voltage, and therefore a non-zero electrical resistance, even if the temperature could somehow be reduced to absolute zero; It only becomes noticeable for wires below about 30 nm in size, but may have to be taken into account in future advanced superconducting computers.
@ References: Dayo et al PRL(98) + pn(98)feb [friction]; Geim et al Nat(98)nov + pn(98)nov [anti-Meißner effect]; Lau et al PRL(01) [QPS]; Chiao a1011 [test of superluminality of supercurrents]; Eschrig PT(11)jan [spin-polarized supercurrents]; Bru & de Siqueira RVMP(13) [Meißner effect, from first principles]; Hirsch a2001 [dissenting view on Meißner effect]. > s.a. photon phenomenology [analogous photon pairing];

Applications > s.a. casimir effect; electronic technology.
* SQUIDs: (Superconducting Quantum Interference Devices) Used to measure tiny variations in magnetic fields (Earth, human brain,...); It can also be applied to gravitational radiation detection.
* Other: Electromagnets; Josephson computers; > s.a. neutron stars.
@ References: Beaugnon & Tournier Nat(91)feb [self-levitating cable]; de Matos a0705 [gravitoelectrodynamic properties?]; Everitt NJP(09) [quantum-to-classical crossover].

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