Superconductivity

In General
* 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: In low-temperature superconductors, pairs of electrons condense into a macroscopically coherent quantum state, which manifests itself as a resistanceless fluid (Bose condensation of Cooper pairs); A non-perturbative effect.
* History: 1911, Discovery by Heike Kamerlingh Onnes in Leiden; 1935, F&H London phenomenological model, containing a field penetration depth ; 1950, Landau-Ginzburg model; 1953, Pippard's coherence length ₀, 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.
@ History: Sauer AHES(07)phy/06 [and Einstein, 1919-1922].

Theory > s.a. types of superconductors.
* Landau-Ginzburg model: A phenomenological model for superconductivity, based on a macroscopic wavefunction , with a dimensionless parameter . This defines the Ginzburg-Landau coherence length := /.
* BCS: The phonon-electron coupling, at a critical T_c, produces a superconducting state with the right values of , coherence length , penetration depth , and critical field H_c.
* Cooper pairs: Bound pairs of free electrons with opposite spins and, in the absence of applied currents or magnetic fields, equal and opposite momenta, that condense into a single macroscopic state described by

(r, t) = |(r, t)| exp{i (r, t)} ;

the phase is coherent throughout the superconductor; They are the basis of the BCS theory.
* Abrikosov: In type II superconductors, for k > 2^1/2, a field H > H_c1 would penetrate in the form of tubes of quantized flux, but the material would remain superconducting up to H = H_c2.
@ General references: Feynman RMP(57); Bardeen, Cooper & Schrieffer PR(57), PR(57); Cooper AJP(59); Bogoliubov ed-62 [reprints]; Balian et al PRP(99) [extension]; Rubinstein & Sternberg JMP(05) & issue [Ginzburg-Landau model]; Butch et al AJP(08)RL.
@ Texts: London 61, 64; Blatt 64; Kuper 68; Tinkham 75; Vidali 93 [I]; Poole et al 95; Ginzburg & Andryushin 04; Annett 04 [intro].
@ Related topics: Hirsch PLA(03) [and Lorentz force]; Pan JMP(03) [near critical T]; Brandão NJP(05) [order parameter and entanglement].

Properties, Effects > s.a. electricity [London's equations]; locality.
* And magnetic fields: The presence of an H above some H_c< 1 kG destroys the superconducting properties of the "soft" superconductors (Pb, Sn,...); Explained by W Meissner and R Ochsenfeld [@ Nat(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, T_c scales with isotopic mass as M^–1/2, suggesting that phonons participate in the phenomenon.
* Josephson effect: The tunneling effect proposed by Brian Josephson of Cooper pairs between two superconductors separated by a thin insulator, maintaining phase coherence between the two superconductors; The difference between the phases on the two sides is related to the supercurrent I through the barrier by sin = I/I₀, where I₀ is the critical current, the maximum current that the junction can sustain; A device based on this effect is a Josephson junction.
* 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; Only becomes noticeable for wires below about 30 nm in size, but may have to be taken into account in future advanced superconducting computers.
@ Josephson effect: in Tinkham 75; Anandan & Pati PLA(97) [geometry].
@ Related topics: Dayo et al PRL(98) + pn(98)feb [friction]; Geim et al Nat(98)nov + pn(98)nov [anti-Meißner]; Lau et al PRL(01) [QPS].

Applications > s.a. casimir effect; electronic technology; types of superconductors.
* 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; neutron stars.
@ References: Beaugnon & Tournier Nat(91)feb [self-levitating cable]; de Matos a0705 [gravitoelectrodynamic properties?].

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