# What is the 'super' parameter of superconductivity and what is the role of Cooper pair?

Only thing I know about superconductors is that here the electrical current face zero resistance. My first question is what is 'super' (physical or mathematical entity) about a superconductor. Or more precisely if I start from the Hamiltonian for a system, which parameter I should try find out to see whether the system is superconducting or not? I read about the mechanism involving the formation of Cooper pair. I understand how they are formed, but don't understand why the pair formation is required for superconductors. Or in other words, how does the pair formation lead to a dissipationless current?

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It's super just because it doesn't behave like a regular conductor but it expels magnetic field (Ochsenfeld effect) and has zero resistivity. You need both to call a material superconductor. –  Ignacio Vergara Kausel Oct 26 '13 at 20:48
The question seems to presume that the adjective "super" has a precise meaning as applied to numbers regardless of context. If you just want a parameter that gets numerically large, take the conductivity. And, yes, that's a trivial suggestion but then in that interpretation it is a trivial question. –  dmckee Oct 27 '13 at 3:35
@dmckee Thanks for the answer. Can you elaborate a little more. Assuming the starting point to be a Hamiltonian (1st or 2nd quantised), what operator I should try to evaluate and what is the difference expected from that of a metal. I am looking for an analytical expression than numbers. Can you give some reference. –  Sumit Oct 28 '13 at 11:45

Historically, european were saying supra-conductors, not super-conductor (it is still supraleitung in german, supraconductivité in french, and something similar in russian, but I don't know cyrillic, have fun checking this issue using Wikipedia and changing the language). Only americans were saying super-conductors at the begining (I guess, since I do not really know why the name changed along time, could be interesting to ask on this website if someone knows...). Supra means beyond or something like that : english speakers still use the preffix supra in supra-natural for instance. One usually opposes supra-/super-conductors to the normal ones. So supra-/super-conductivity means the conductivity of the material is not the natural/normal one: supra-/super-conductors do not follow the Ohm's law $j=\sigma E$ relating the current $j$ to the electric field $E$ through the conductivity tensor $\sigma$, as we expect in normal materials. Historically, normal was refering to everything known at that time.