|  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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