# What is the explanation of BCS theory for the zero resistance of superconductors?

While BCS theory's predictions like isotope effect are excellent, I could never completely understand what is the origin of zero resistance in superconductors according to BCS theory. Any advice?

## All Answers (11)

Yatendra Singh Jain· North Eastern Hill UniversityYatendra Singh Jain· North Eastern Hill UniversityAk Rajarajan· Bhabha Atomic Research CentreAnswering 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.

Yatendra Singh Jain· North Eastern Hill UniversityE. Schachinger· Graz University of Technologykind 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.

Je Huan Koo· Kwangwoon UniversityYatendra Singh Jain· North Eastern Hill UniversityEdgar J. Patiño· Los Andes University (Colombia)Thomas Scheller is right.

Je Huan Koo· Kwangwoon UniversityTo 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.

Can you help by adding an answer?