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 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].

**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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