What is the “BCS Cooper pair condensation” as a physical phenomenon in terms of experiments?

Question

"Thought" experiments and "numerical" experiments are allowed.

This question is motivated by the question Has BCS Cooper pair condensate been observed in experiment? , and by our recent research on anyon superfluidity where anyons are emergent from a fermion system.

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user Xiao-Gang Wen

Comments

Would the question be better stated "What observables are indicative of BCS Cooper pair condensation?" (which is how the title reads to me) or is it "Has BCS Cooper pair condensation been observed?" (which is closer to how I read the body)?

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user dmckee

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Can be this article be a possible answer?

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user DaniH

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The question is "What observables are indicative of BCS Cooper pair condensation?" The body just contains the motivation of the question.

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user Xiao-Gang Wen

Answer 1

Isn't the proximity effect a delocalization of the condensate outside the superconductor ? Then, one can probe this effect via tunnelling (density of state probe).

Vortex are also an inhomogeneity of the condensate that one can easily visualise (STM, X-ray, ...).

Well, any kind of inhomogeneity can be seen as I believe. But I do not know of an experiment probing the stable, constant condensate (each time, one needs phase gradient in what I know).

It may also be possible to probe the edge currents proposed by London long ago (I'm not aware of such a detection, nor of an actual experiment).

EDIT: Ok, an other way of answering, I may have misunderstood the question. After reading this topic, maybe some better answers would be:

1) The coupling of two electrons to form a bound state, mediated by a phonon (à la Cooper / Bardeen and Schrieffer). So in principle one could generate it by phonon excitations (already done in the 70's if I remember correctly)

2) The emergence of a macroscopic quantum state from interacting electrons, and the creation of a quantum macroscopic state with all electrons sharing the same phase. So in principle one could observe the growing of the phase rigidity.

3) The emergence of a gapped excitation at the Fermi level.

But I still believe the question is not clear ... :-( Well, as it must at the beginning of organising minds :-)

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user FraSchelle

Comments

I think most of the above proposals measure the off diagonal long range order $<c_x c_{x+\delta}c^\dagger_0 c^\dagger_{\delta}>$. The real issue is that the appearance of fermion-pair off diagonal long range order may not imply the “BCS Cooper pair condensation". The state may be an exotic superconducting states. How to rule that out?

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user Xiao-Gang Wen

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@Xiao-GangWen Ok, good point. I was thinking that the exotic states were not real problem. They indeed fall into the given experiments detecting scheme. I was thinking they are also "Cooper pair condensation" plus extra features (higher crystal-like symmetries for instance). So you want to discard them... but why ?

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user FraSchelle

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It is a matter of definition. I thought “BCS Cooper pair condensation” does not contain all the possible exotic SC states, which may contain all kind of emergent fractional statistics (ie with non-trivial topological orders). Certainly, if one define “BCS Cooper pair condensation” as off diagonal long range order in $< c_xc_{x+\delta}c^\dagger_0c^\dagger_\delta >$, then your proposals are valid.

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user Xiao-Gang Wen

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@Xiao-GangWen Sorry I was not explicit enough. I understand your point. You want to isolate the, say, "old-fashionned" BCS states (I would call it s-wave SC in metal, since I'm not even sure you want it to exist in alloys) from the "modern topological" version of the theory. I nevertheless believe these two guys are just brothers. In short, they have some common phenomenology, and the topological states have something more (I still wonder what ?). So I'm wondering why do you want to separate them, instead of classifying them ?

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user FraSchelle

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So, to continue my point, the family includes: boson superfluidity (well H4) corresponding to a fluid BEC of bosons ; fermion superfluidity (well H3) corresponding to "pairing" of fermions ; superconductivity corresponding to a charged superfluidity (then the phenomenology is totally different, having Higgs-Bogoliubov-Anderson ... ) of defined spin ; superconductivity +, say, corresponding to spin fuzziness (or if you prefer to the breakdown of the usual fermion/boson duality). The last point is not entirely clear for me, but you should the one able to complete :-). Now each step has its...

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user FraSchelle

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... own phenomenology, from the simpler (frictionless displacement and mechanical vortex) to the charge (the one above + EM vortex, Josephson and Meissner) to the topological effect (... and then what new ?, sorry for my ignorance about this point). I'm also wondering about the difference between $^{3}He$ and $^{4}He$ superfluidity phenomenology, maybe a good point to start with...

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user FraSchelle

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Thanks for the comments. It reveals one important point. By definition, "BCS Cooper pair condensation" only describe those SC states that are describable by quadratic effective Hamiltonians $H_{eff}=\sum c_i^\dagger c_j + c_i c_j +h.c.$. Both "old-fashionned" BCS states and new "topological superconductors" are "BCS Cooper pair condensation" in this sense. But there are strongly interacting superconductors which may contain more exotic topological orders that can never be described by quadratic effective Hamiltonians. Do we have an experimental way to seperate the two kinds of SC states?

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user Xiao-Gang Wen

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@Xiao-GangWen Well, for the moment I only see the critical (for strongly interacting, say) vs. Gaussian (for quadratic mean-field) fluctuation exponents at the transition. It should be very unlucky that they match, isn't it ? (NB: The situation is more complicated in practise, since really close to the BCS transition, Gaussian fluctuations are no longer a good approximation, cf. Ginzburg-Levanyuk criterion)

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user FraSchelle

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Here we only concern about the kinds of SC states. We do not concern about the phase transitions, which is a totally different issue. "What observables are indicative of BCS Cooper pair condensation?"

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user Xiao-Gang Wen

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@Xiao-GangWen Pfiou, it's become too difficult for me then :-) I don't have immediate answer, sorry. But I would be happy to know more about that.

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user FraSchelle

Answer 2

This answer, which in essence is not really mine, is intended to understand a bit better what the actual question is really about. I was opening the Feynman's book a few days ago and I remembered this question. Let's see if Feynman can help us :-)

Feynman, in his book Statistical physics - A set of lectures wrote a section entitled 10.8 - Real test of existence of pair states and energy gap which might be of interest for you.

To give you the idea developed there, let me copy a few sentences:

Any phenomenon in which scattering of electrons is involved will serve as a test for the existence of the pair states. Attenuation of phonons and paramagnetic relaxation are examples. […]

When the pair states proposed in the BCS theory exist, a scattering of an electron $k\uparrow$ induces an interference with the paired electron at $-k\downarrow$ […]

Let us now discuss gap experiments. [… then Feynman describes the tunnelling experiment to measure the DOS ...]

My feeling is that Feynman captures the essence of the BCS Cooper pair condensate. But it also seems to me that this is precisely this notion which is unclear.

This post imported from StackExchange Physics at 2014-04-04 16:22 (UCT), posted by SE-user FraSchelle