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The conceptual model I have been introduced to for cooper pairs in a bulk superconductor is what I would call the "wake" model, where one electron deforms the positively charged lattice, changing the potential energy landscape and causing the second electron to be drawn closer.

This seems like a terrible conceptual picture both because the electrons in a superconductor should have a well defined localized wave function and because the ground state of the BCS theory has zero net momentum, which would suggest they orbit around each other or something...

If anyone can explain how I should be thinking about this I would be very grateful.

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  • $\begingroup$ I have always thought the "wake" model was suited only to explain how it is you ended up with a local attractive force between electrons, when you start with the Coulomb interaction which is non-local and repulsive. Getting from a local attractive interaction to superconductivity is not something I have ever seen a nice classical picture for, nor is it the kind of thing you expect a nice classical picture for. By the by, you mention a picture where the electrons orbit each other, but remember, in regular SC the cooper pairs have zero-angular momentum. $\endgroup$
    – BebopButUnsteady
    Jul 12, 2011 at 18:16

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It is an incorrect picture to envision the Cooper pairs as existing as an isolated occurrence in a lattice, since the very existence of Cooper pairs depends on a supporting cast of other electrons. In his work, Cooper showed that the ground state of a metal is unstable against an arbitrarily small net attraction between two electrons of opposite momentum, with this momentum near the Fermi momentum of the system. Therefore, the energetically favorable state is the paired state, and the superconducting state exists when all of the conduction electrons are bound into such pairs.

Further, something which is under-emphasized in the "wake model" is the size of the Cooper pairs in "classical" superconductors (ie, superconductors that have the pairing mechanism described by BCS theory). The spatial extent of Cooper pairs is quite large, on the order of thousands of angstroms (many, many lattice spacings), meaning that the pair condensation results in millions (or more) over lapping pairs.
In effect, in the superconducting state, these millions of paired electrons travel like a superfluid through the material.

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    $\begingroup$ There is eventually a simpler vision about that, perhaps too much radical. It consists in saying that superconductivity does not appear in real space, it appears in reciprocal (momentum) space. One needs a Fermi sea and two electrons at opposite momenta. Then, it's relatively easy to make them condensing, since the Fermi energy is huge, whereas the ground state of boson field is zero. $\endgroup$
    – FraSchelle
    Dec 9, 2012 at 22:30
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    $\begingroup$ There is a very important element which is missing in that picture. That is the Pauli exclusion principle: it is crucial to see that this principle produces an effective two-dimensional surface for the motion of a pair of two added electrons. It is because of this two-dimensionality that they could bind in a bound state given any weak attraction. This is not true for higher-dimension. $\endgroup$
    – hyd
    Sep 13, 2014 at 6:36

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