Editing Superconductivity (section)

=== Conventional theories (1950s) ===
During the 1950s, theoretical [[Condensed matter physics|condensed matter]] physicists arrived at an understanding of "conventional" superconductivity, through a pair of remarkable and important theories: the phenomenological [[Ginzburg–Landau theory]] (1950) and the microscopic BCS theory (1957).<ref>{{cite journal |author=Bardeen |first1=J. |last2=Cooper |first2=L. N. |last3=Schrieffer |first3=J. R. |name-list-style=amp |date=1957 |title=Microscopic Theory of Superconductivity |journal=[[Physical Review]] |volume=106 |issue=1 |pages=162–164 |bibcode=1957PhRv..106..162B |doi=10.1103/PhysRev.106.162 |doi-access=free}}</ref><ref name="BardeenCooperSchrieffer2">{{cite journal |author=Bardeen |first1=J. |last2=Cooper |first2=L. N. |last3=Schrieffer |first3=J. R. |name-list-style=amp |date=1957 |title=Theory of Superconductivity |journal=[[Physical Review]] |volume=108 |issue=5 |pages=1175–1205 |bibcode=1957PhRv..108.1175B |doi=10.1103/PhysRev.108.1175 |doi-access=free}}</ref>

In 1950, the [[Phenomenology (particle physics)|phenomenological]] [[Ginzburg–Landau theory]] of superconductivity was devised by [[Lev Landau|Landau]] and [[Vitaly Ginzburg|Ginzburg]].<ref>{{cite journal |author=Ginzburg |first1=V. L. |last2=Landau |first2=L. D. |name-list-style=amp |date=1950 |title=On the theory of superconductivity |journal=[[Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki]] |volume=20 |page=1064}}</ref> This theory, which combined Landau's theory of second-order phase transitions with a [[Schrödinger equation|Schrödinger]]-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, [[Alexei Alexeyevich Abrikosov|Abrikosov]] showed that Ginzburg–Landau theory predicts the division of superconductors into the two categories now referred to as Type&nbsp;I and Type&nbsp;II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau had received the 1962 Nobel Prize for other work, and died in 1968). The four-dimensional extension of the Ginzburg–Landau theory, the [[Coleman–Weinberg potential|Coleman-Weinberg model]], is important in [[quantum field theory]] and [[cosmology]].

Also in 1950, Maxwell and Reynolds et al. found that the critical temperature of a superconductor depends on the [[Isotope|isotopic mass]] of the constituent element.<ref>{{cite journal |author=Maxwell |first=E. |date=1950 |title=Isotope Effect in the Superconductivity of Mercury |journal=[[Physical Review]] |volume=78 |issue=4 |page=477 |bibcode=1950PhRv...78..477M |doi=10.1103/PhysRev.78.477}}</ref><ref>{{cite journal |author=Reynolds |first1=C. A. |last2=Serin |first2=B. |last3=Wright |first3=W. H. |last4=Nesbitt |first4=L. B. |name-list-style=amp |date=1950 |title=Superconductivity of Isotopes of Mercury |journal=[[Physical Review]] |volume=78 |issue=4 |page=487 |bibcode=1950PhRv...78..487R |doi=10.1103/PhysRev.78.487}}</ref> This important discovery pointed to the [[electron]]–[[phonon]] interaction as the microscopic mechanism responsible for superconductivity.

The complete microscopic theory of superconductivity was finally proposed in 1957 by [[John Bardeen|Bardeen]], [[Leon Neil Cooper|Cooper]] and [[John Robert Schrieffer|Schrieffer]].<ref name="BardeenCooperSchrieffer2" /> This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972.

The BCS theory was set on a firmer footing in 1958, when [[N. N. Bogolyubov]] showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic [[Hamiltonian (quantum mechanics)|Hamiltonian]].<ref>{{cite journal |author=Bogoliubov |first=N. N. |date=1958 |title=A new method in the theory of superconductivity |journal=[[Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki]] |volume=34 |page=58}}</ref> In 1959, [[Lev Gor'kov]] showed that the BCS theory reduced to the Ginzburg–Landau theory close to the critical temperature.<ref>{{cite journal |author=Gor'kov |first=L. P. |date=1959 |title=Microscopic derivation of the Ginzburg–Landau equations in the theory of superconductivity |journal=[[Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki]] |volume=36 |page=1364}}</ref><ref name="BCS-boboliubov2">{{cite journal |author=Combescot |first1=M. |last2=Pogosov |first2=W. V. |last3=Betbeder-Matibet |first3=O. |date=2013 |title=BCS ansatz for superconductivity in the light of the Bogoliubov approach and the Richardson–Gaudin exact wave function |journal=Physica C: Superconductivity |volume=485 |pages=47–57 |arxiv=1111.4781 |bibcode=2013PhyC..485...47C |doi=10.1016/j.physc.2012.10.011 |s2cid=119121639}}</ref>

Generalizations of BCS theory for conventional superconductors form the basis for the understanding of the phenomenon of [[superfluidity]], because they fall into the [[lambda transition]] universality class. The extent to which such generalizations can be applied to [[Unconventional superconductor|unconventional superconductors]] is still controversial.