Timeline for What observables are indicative of BCS Cooper pair condensation?
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| Apr 13, 2017 at 12:40 | history | edited | CommunityBot |
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| Mar 28, 2013 at 12:45 | comment | added | FraSchelle | @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. | |
| Mar 26, 2013 at 18:29 | comment | added | Xiao-Gang Wen | 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?" | |
| Mar 26, 2013 at 16:03 | comment | added | FraSchelle | @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) | |
| Mar 26, 2013 at 13:31 | comment | added | Xiao-Gang Wen | 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? | |
| Mar 26, 2013 at 9:44 | comment | added | FraSchelle | ... 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... | |
| Mar 26, 2013 at 9:43 | comment | added | FraSchelle | 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... | |
| Mar 26, 2013 at 9:32 | comment | added | FraSchelle | @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 ? | |
| Mar 26, 2013 at 1:31 | comment | added | Xiao-Gang Wen | 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. | |
| Mar 25, 2013 at 5:19 | comment | added | FraSchelle | @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 ? | |
| Mar 25, 2013 at 0:43 | comment | added | Xiao-Gang Wen | 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? | |
| Mar 24, 2013 at 19:31 | history | edited | FraSchelle | CC BY-SA 3.0 |
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| Mar 24, 2013 at 19:08 | history | answered | FraSchelle | CC BY-SA 3.0 |