It is understood that when a material is cooled below certain temperature it loses its resistivity. Why do we think in terms of matter nature of electrons. Superconductivity is transmitted by massive photons and not electrons. Massive photons (bosons) travel without attenuation carrying the electromagnetic energy embedded in the system.
When the symmetry is broken, at the onset of superconducting state, photons become massive. The fields are found to to obey the Klein-Gordon equation instead of a pure massless wave (light). I see that the whole stuff is a transportation of energy. Moreover, the critical quantum conductivity is 2m/mu_0h, h:Planck constant, mu_0 permeability of space and m is the mass of the particle that induces the superconductivity.
Can we say that in superconductor we have current without voltage, and in Josephson effect a current without voltage? Can we say that these two effects are conjugate (complement) to each other?
Elemetary excitations of the solid are not electrons. They might be quasiparticles called "electrons" (normally) or quasiparticles of other nature, eg cooper pairs. Resistance is determined by scattering. Wave functions do not attenuate. they are scattered into each other. Superconductivity arises when the scattering of quasiparticles is forbidden. Due to the gap in the spectrum. At low temperaure quasiparticles cannot get energy to breach the gap.
Superconductivity can be described by a wavefunction with an attractive potential for a pair of electrons with certain coherence lenght (see for example P. DeGennes Book) so a wave with a state of two electrons describes the phenomenon (Cooper wrote the paper)... now if we want to see is a cuasiparticle phenomenon, it can be used instead a Cooper pair as a a cuasiparticle.
Dear Igor,
I trust what is called the quasi-particle is our massive photon (boson). When appeared superconductivity is described by the Klein-Gordon equation rather than by Maxwell equations that are valid for massless photons. What do you think?
Dear Arbab, Maxwell equation (third one) can describe superconductivity mediated by phonons as well, as if they were photons...
That is really very interesting but do phonons have electromagnetic character?
Superconductivity is always related with the bosonization of the conducting electrons and no with the mass of the photons. It is true that Meissner effect (diamagnetic behaviour) distinguish a superconductor from a perfect conductor, but this effect is very well explained since a long time ago for the two London equations which only use the mass of the electrons and Maxwell equations. The electric currents screen the external magnetic field creating a new one equal magnitude but in opposite direction on its surface, i.e. they cancel each other.
It is true that the superconducting state breaks breaks spontaneously the global U(1) gauge symmetry (to Z2 in fact) to give Goldstone particles which allow to provide a massive photons. But this is only related with the behaviour of the superconductor under a magnetic field and no with the superconducting phase as Cooper pairs of electrons (bosons) close to the Fermi level. This is exactly the mechanism taken in particle physics associated to the Higgs field.
I hope it helps.
Concerning the Meissner effect I found an explanation using classical physics only:
Article Meissner Effect in Classical Physics
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