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    $\begingroup$ 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? $\endgroup$
    – Xiao-Gang Wen
    Commented Mar 25, 2013 at 0:43
  • $\begingroup$ @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 ? $\endgroup$
    – FraSchelle
    Commented Mar 25, 2013 at 5:19
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    $\begingroup$ 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. $\endgroup$
    – Xiao-Gang Wen
    Commented Mar 26, 2013 at 1:31
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    $\begingroup$ 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? $\endgroup$
    – Xiao-Gang Wen
    Commented Mar 26, 2013 at 13:31
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    $\begingroup$ 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?" $\endgroup$
    – Xiao-Gang Wen
    Commented Mar 26, 2013 at 18:29