Zero resistivity in superconducting state

[vatlychatran]

Hi everyone,
- Could you explain for me the meaning of "net" in the phrase "small net attraction between electrons" in superconductivity, (or synonym of it)?
- We usually say that BSC theory explains the superconductivity of conventional superconductors, one feature of superconductivity is zero resistivity at temperature below Tc, but I don't know how Cooper pair formation and energy gap explain this behavior explicitly, Is there any formula of resistivity which includes superconducting gap? To explain resistivity in normal state we say that there are collisions between electrons and defects, lattice but why can't we imagine Cooper pair as a particle which also collides with defects and lattice?
(In books on superconductivity author usually derive energy gap and say that there is no collision without proving)
Thank you very much.

 

[DrDu]

In a superconductor electrons on one hand side repell each other due to Coulombic forces. On the other hand there is attraction due to the exchange of phonons. Only for some frequency and wavevector values of the electrons the attraction is stronger than the repulsion. Hence net attraction.

The explanation for infinite conductivity is not straight forward. Also Cooper pairs scatter and get broken up. In contrast with a metal, where the electrons can get scattered to the "backside" of the Fermi surface, thus reducing the net current, in a superconductor there are no states on the backside due to the gap. Hence scattering cannot reduce net current. The excited or broken up Cooper pairs will sooner or later relax back to the original Cooper pairs forming the condensate.