BCS theory has several flaws and it does not provide complete, clear and experimentally consistent microscopic understanding of the phenomenon. In fact it is now clear that it does not have potential to even explain the superconductivity of normal (metals and their alloys) superconductors. So it is difficult to understand loss of resistance in terms of BCS theory. As shown in ( http://www.scribd.com/doc/110441679/Intrinsic-Problems-Superfluid-Theories ), the formulation of theory has intrisic problems for which it has all its weaknesses. However, if you want to understand why loss of resistance then read another paper [ http://www.scribd.com/doc/110681115/First-Quantization-Theory-of-Superconductivity ] which can explain even to a layman why loss of resistance in superconducting state. If you have any question regarding these papers and their analysis you can also contact me personally my email given in the first/second paper.

Thomas Scheller is perfectly right in putting an account available from the BCS theory. However, there are certain confusions in the BCS account. If two electrons in a pair have equal and opposite momenta how do they contribute to finite supercurrent ? If two electrons in Cooper pair make a single bound unit like a diatomic molecule, do these electrons have momentum as their good quantum number ? If not how could the BCS account in terms of well defined momenta k and -k be justified. It is well known that atoms in a diatomic molecule can have a well defined discrete energy but in any such quantum state they do not have well defined momenta. Since two electrons in Cooper pair are concluded to have k and -k momenta, how do they move in coherence as observed experimentally in case of suppercurrents. Thus BCS theory seem to provide answers to several important questions in isolation. The confusion arises when we seek answers to a chain of questions. Let me underline the fact that BCS theory is a mathematically sound theory but it has serious weaknesses because its basic premises have intrinsic probelms and inconsistencies with physical realities of electron fluid [particularly at low temperature] in a conductor as concluded in my earlier comment to this question.

Thanks to Thomas Scheller for the nice explanation. The confusion still remains because presence of a band gap is the reason given for why semiconductor (insulator) is semiconducting (insulating). Larger the gap worse conductor it is! Now there seems to be no special reason for superconducting gap to produce zero resistance and not an insulating state! In my opinion being able to scatter the electron to an excited state easily is the essential reason for conductance in metals. If you remove this property from a metal by adding a gap in the energy states, one should be getting an insulating state.

Answering Jains question, k , -k variation is not very strict in BCS theory and it allows a variation in k and -k before the pair is broken. I suppose this could explain a supercurrent.

I would simply restate that quantum states of electrons (in particular at low temperature and superfluid state) can not be identified by their momenta; I understand the variation that Rajarajan is talking about and a careful thinking would surely lead him to realise that it corresponds to nothing but the center of mass momentum of two electrons presumed to be in a k, -k pair state.

I agree very much with what has been said by Thomas Scheller. The same

kind of argument can be found in the book by G. D. Mahan "Many-Particle

Physics", Plenum Press (London 1981), page 793. This argument explains

nicely why we have zero resistance below T_c when dealing with dc-currents.

But we can go to a more general argument. There is the famous Ferrell-Glover-

Tinkham sum rule (FGT) [R.A. Ferrell and R.E. Glover, Phys. Rev. 109, 1398 (1958);

M. Tinkham and R.A. Ferrell, Phys. Rev. Lett. 2, 331 (1959)] which states that

the integral from zero frequency to infinite frequency over the real part,

\sigma_1(\omega,T), of the complex optical conductivity \sigma(\omega,T) is

proportional to the square of the plasma frequency. This holds independently

for the normal as well as the superconducting state. If we stick to s-wave

superconductivity (classical BCS) then \sigma_1(\omega,T) develops an 'optical'

gap of twice the superconducting energy gap, i. e. 2\Delta(T). Thus, for

\omega = 0+\epsilon (\epsilon infinitesimal) to \omega = 2\Delta(T)

\sigma_1(\omega,T) is zero. This is in contrast to the normal state in which

\sigma_1(\omega,T) is certainly not zero in this regime. If \sigma_1(\omega,T)

doesn't overshoot substantially the normal state \sigma_1(\omega,T) for

\omega > 2\Delta(T) the FGT sum rule seems to be violated. (This is not observed.)

As the FGT sum rule is just another formulation of an energy conservation law,

the way out of this dilemma is that there has to be \delta-distribution at zero

frequency in \sigma_1(0,T) in the superconducting state. Its weight is determined by

the 'missing area' in \sigma_1(\omega) between normal and superconducting state.

Such a \delta-distribution in \sigma_1 at zero frequency describes zero resistance for

dc-currents. This argument has nothing to do with BCS theory. The nice thing about BCS theory is, that it can help to calculate just this missing area. Of course not exact

in a quantitative way because BCS is not a quantitative theory. If one wants to do

quantitative work one has to go beyond BCS but this is not required for a basic

understanding.

I may explain normal electrons in superconducting states to show no resistance as attached file such as

It appears that above mentioned paper by Koo and Kim also questions the BCS theory as their results have significant difference with it about the Band gap. This underlines our conclusion that BCS type theories can not reveal complete, clear and experimentally consistent understanding of the phenomenon for their intrinsic problems; this has been concluded in [ http://www.scribd.com/doc/110441679/Intrinsic-Problems-Superfluid-Theories ]. In addition we also conclude that certain experiments unequivocally conclude that BCS theory is not valid even for metallic superconductors as insisted after the discovery of HTC superconductors. Please see [ http://www.scribd.com/doc/146390067/On-the-origin-of-de-Heer-effect-and-the-accuracy-of-microscopic-theories-of-superconductivity ]. I hope this reality would be accepted soon by the physics community in the interest of establishing the origin of the phenomenon.

Thomas Scheller is right.

To help understanding, I attach a file.

The content of my paper discuss

the bandgap in normal states is converted into superconducting reservoir containing normal electrons above Fermi level at superconducting phases to have no resistance.