Types of Superconductors  

In General
* Type I: The ones in which λ < ξ; They have positive wall energy and are not so useful, they can't be used for magnets.
* Type II: The ones in which λ > ξ; They have negative wall energy, maximize surface and create vortices, quantized in units of φB = hc/2e; This type includes all high-Tc superconductors.
* BCS vs unconventional (non-BCS): In conventional (BCS) superconductors the pairing interaction arises from lattice distortions, in other superconductors the mechanism is different; For example, there is evidence that ferromagnetic fluctuations provide the pairing force in UCoGe.
* Examples: The heavy fermion compound UPt3; UCoGe, an exotic type in which ferromagnetism and superconductivity seem to happily coexist.
@ Various materials: news pw(02)jan; Canfield & Bud'ko SA(05)apr [MgB2]; Michelle Phy(08) [iron pnictides and other iron compounds]; Day PT(09)aug [iron-based]; Donnelly PT(09)oct [He, Tisza's contributions]; Julian Phy(02)feb [UCoGe]; Dave et al PRL(13) + news(13)mar [cuprates, current and Luttinger's theorem]; Song et al PRL(16) + Phy(16) [two distinct mechanisms in FeSe]; news Phys(20)feb [twisted bilayer graphene].
@ Unconventional: Scalapino RMP(12) [arguments for pairing mediated by spin fluctuations].
@ Other special types: Arutyunov et al PRP(08) [1D systems].

High-Temperature Superconductivity > s.a. Insulators.
* History: 1986, Discovery and almost immediate hopes for room-temperature superconductors; 2004, 2016, Still not completely understood and no Tcs near room temperature; Theorists suspect that metallic hydrogen might be superconducting at room temperature; 2019, Simulations with lattices ultracold atoms playing the role of electrons with tunable parameters may provide clues.
* Properties: Usually very anisotropic (the energy gap is direction-dependent).
* Mechanism: 2004, It is widely believed that the classic BCS theory cannot explain it; Cooper pairs are involved but it is not clear what holds them together; There are claims that interactions between phonons and electrons or magnetic resonances are relevant, but recent experiments seem to rule those explanations out; 2008, Electron-phonon interactions can only account for a fraction of the behaviour; 2017, Cuprates (Tc = 134 K) have vortex states, so they may be conventional superconductors after all.
* Examples: The most common one by far is YBCO (YBa2Cu3O7).
@ Books, reviews: Ginzburg SPU(91) [rev]; Cyrot & Pavuna 92; Holton et al AS(96)jul [discovery]; Nowotny & Felt 02 [r PT(98)mar]; Kresin & Wolf RMP(09) [electron-lattice interaction]; Zaanen a1012-ch [history]; Lederer a2007 [history, on scientific errors].
@ News: Maddox Nat(90)apr; Hamilton Sci(90)oct [Tc = 125 K]; news pw(06)aug [evidence for role of phonons]; news pw(06)sep [decline in number of publications]; news pn(07)jul [and Mott insulator properties]; news PT(08)jan [use on the power grid]; news pw(08)apr [not explained by phonons]; Norman video Phy(10) [layered iron arsenides]; Bovensiepen Phy(10)aug [relaxation of excited electrons and phonons]; news pw(10)aug [role of fractals]; news mt(11)apr [role of next-nearset neighbor interactions in superconductivity in iron-based compounds]; news caltech(11)dec [proposed explanation]; Dal Conte et al sci(12)mar + news PhysOrg(12)mar [fine-grained data on electron relaxation its effects on the superconductor]; news at(12)jun [quantum fluctuations rather than changes in temperature or pressure may be a key]; news ls(13)aug [unexpected magnetic excitations]; news pw(15)aug [hydrogen sulfide becomes superconducting at a record 203 K (–70 °C), when under a pressure of 1.5 million bar]; Song & Xue Phy(17) [re cuprates]; Somayazulu et al PRL(19) + news sn(18)sep [high-pressure lanthanum-hydrogen compounds, 260 K]; news Phy(19) [simulation using a lattice of ultracold atoms]; news Phy(19)aug, sn(19)aug [proposed, above room T, superhigh p]; news sn(20)apr [pair-density wave seen in cuprate]; news sn(20)oct [squeezed C, H and S at very high pressures, 15°C].
@ Theory: Davydov PRP(90); Kulic PRP(00); Lanzara et al Nat(01)aug [phonon-electron]; Herbut PRL(05)cm/04 [effective theory]; Alexandrov PS(11) [developments in the bipolaron theory]; Sachdev PRX(15) [entropy, and Bekenstein-Hawking entropy]; > s.a. physical theories [scientific pluralism].

In Particle Physics and Field Theory > s.a. cosmic strings [superconducting]; QCD [vacuum].
* Color superconductivity: A property of the ground state of QCD at high densities and low temperatures, believed to involve Cooper pairs of quarks.
@ Color superconductivity: Shovkovy FP(04) [lectures]; Alford et al RMP(08)-a0709 [in dense quark matter]; Anglani et al RMP(14) [and astrophysics].
@ Holographic superconductors: Horowitz LNP(11)-a1002 [introduction]; Brito et al PLB(14)-a1211 [domain-wall description of superconductivity]; Musso a1401-ln [intro].

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