A What Physical Evidence Supports the Role of Cooper Pairs in Superconductivity?

[fluidistic]

I am wondering what is the physical evidence that Cooper pairs are indeed the ones responsible for superconductivity. These pairs consist of two electrons with opposite momentum, forming a boson with null momentum.
But what about pairs that would consist of, say, 6 electrons (or even more)? Of these 6 electrons, 3 (with momenta -p, -p, +p) would form a fermion with momentum -p while the 3 other electrons would form a fermion with momentum +p (because of -p, +p, +p). Hence such a pair would also form a boson with null momentum, just like a Cooper pair does.

I could understand that since the pairs are formed with an interaction between electrons via virtual phonons, such a pair would be much less likely to form than a regular Cooper pair. But is the probability of such a pair to form exactly 0? If not, would such a pair contribute to superconductivity? I guess not, since it is claimed everywhere that only Cooper pairs are responsible for superconductivity.

So, which phenomenon, or experiment, invalidates all other possible pairing of electrons? Or what prediction(s) would such pairs do that doesn't match experiments?

 

[f95toli]

I'm not sure there is a single experiment that would be the final "proof" in this case.
However, there are plenty of experiments which can only be described if you assume quantisation in h/2e; in a normal SC ring made from an s type superconductor you never see quantisation in h/e
On top of that you also have the Josephson effect, which again -usually- has h/2e as a parameter.

You have the fact that 2e enters as a parameter in the BCS theory; and this can be used to calculate e.g. the Tc if you know the gap voltage (or vice versa).

Last but not least you have a variety of tunneling experiments (or even single electron transitors), where you can see a transition from 2e to e as you suppress superconductivity; but never see e.g. a 3e gap.

I could probably think of a few other experiments, this is just what came to mind.

 

[ZapperZ]

In addition to what f95toli has stated, the experimental verification of the pairing symmetry for both conventional and unconventional superconductors indicate that these are e-e pairs. You can't have more than 2 electrons in the pairs to make a singlet-state, a triplet state, and having the s-orbital and d(x²-y²)-orbital symmetry.

The amount of evidence is simply overwhelming here.

Zz.

 

[member659127]

In addition to what f95toli has stated, the experimental verification of the pairing symmetry for both conventional and unconventional superconductors indicate that these are e-e pairs. You can't have more than 2 electrons in the pairs to make a singlet-state, a triplet state, and having the s-orbital and d(x²-y²)-orbital symmetry.

The amount of evidence is simply overwhelming here.

Zz.

Hi, thanks for the nice explanation. I'm a physicist but not an expert in the subject, just curious if you know whether the BCS theory explicitly postulates "the pairs" or proposes a picture of "collective behaviour" of bosons in which case the pairs are the most obvious, the simplest and the most contributng element. (An electron quartet for example would contribute or not to the overall picture... sort of a series expansion thing to make myself more clear)

Sorry if it is a stupid question, recently published some numerical calculations related to this and would like to gain more insight on the subject. I would also appreciate if you know a nice, clean source to learn the theory.

 

[ZapperZ]

Hi, thanks for the nice explanation. I'm a physicist but not an expert in the subject, just curious if you know whether the BCS theory explicitly postulates "the pairs" or proposes a picture of "collective behaviour" of bosons in which case the pairs are the most obvious, the simplest and the most contributng element. (An electron quartet for example would contribute or not to the overall picture... sort of a series expansion thing to make myself more clear)

Sorry if it is a stupid question, recently published some numerical calculations related to this and would like to gain more insight on the subject. I would also appreciate if you know a nice, clean source to learn the theory.

The BCS theory came out of the Cooper model (the "C" in BCS). The thing that isn't explicitly required in BCS is phonons as the "glue", even though that is what was used to calculate the pairing strength. It is why in high-Tc superconductors, some models have replaced the phonon glue with spin-fluctuation/magnetic pairing glue.

Zz.

 

[Henryk]

I would also appreciate if you know a nice, clean source to learn the theory.

The original paper by Bardeen, Cooper and Schriffer !. I think this is the best written scientific paper I've have ever seen. So clearly written, precise language and a complete theory in just one paper.

 

[adench2]

A possibly non-helpful answer is that in the study of condensed matter theory, one can show (via Wick's theorem, etc) that any many-body electronic interaction (such as the 6-electron interaction you propose) integral can be decomposed into a sum of products of 2-electron interaction integrals. Thus the "pair" picture formally can be used to describe your example. So your 6-electron example can be written as 3 sets of Cooper pairs interacting. Wick's theorem is actually a specialization of some results in statistics that I can't recall the details of.

I suggest checking out maybe Mattuck's old book on Many-body Physics and Feynman diagrams, or any other source that goes through this stuff.