Superconductivity |

**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 effec; 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
*ξ*_{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.

@ __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 *T*_{c},
produces a superconducting state with the right values of Δ,
coherence length *ξ*, penetration depth *λ*,
and critical field *H*_{c}; 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* > *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)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 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].

**Properties, Effects** > s.a. electricity [London's
equations]; Josephson Effect; locality; symmetry breaking.

* __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 (or Meißner) and R 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, *T*_{c} 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];
> 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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