A Stability of persistent currents in superconductors regardless of temperature

[Stanislav]

TL;DR Summary

From theories of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly warm up, we must observe a decrease in the actual supercurrent. However, this supercurrent decrease is never observed. Is the superfluid density independent of temperature ?

From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly increase the temperature, we must observe a decrease in the actual supercurrent, because the density of electron pairs and total supercurrent momentum decrease. However, this supercurrent decrease is never observed. Does it mean that the superfluid density is independent of temperature ?

 

[pines-demon]

From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly increase the temperature, we must observe a decrease in the actual supercurrent, because the density of electron pairs and total supercurrent momentum decrease. However, this supercurrent decrease is never observed. Does it mean that the superfluid density is independent of temperature ?

Not an expert here, but how do you know it does not decrease? What size is the ring you are considering?

 

[Stanislav]

Not an expert here, but how do you know it does not decrease? What size is the ring you are considering?

There are always temperature fluctuations in every cryostat, and the SC-density decrease is not very weak, so a current instability would be detectable. However, the current is stable for years. I didn't find in literature any dependence of the supercurrent on temperature. The ring size is like in experiments with persistent supercurrents, macroscopic, a few centimeters.

 

[pines-demon]

There are always temperature fluctuations in every cryostat, and the SC-density decrease is not very weak, so a current instability would be detectable. However, the current is stable for years. I didn't find in literature any dependence of the supercurrent on temperature. The ring size is like in experiments with persistent supercurrents, macroscopic, a few centimeters.

Being naive, London equations (the first macroscopic equations for superconductivity) argue that the current depends on the superconducting density $n_s$ which depends on the temperature.

 

[Stanislav]

Being naive, London equations (the first macroscopic equations for superconductivity) argue that the current depends on the superconducting density $n_s$ which depends on the temperature.

Exactly. Then the question : why is the supercurrent stable in all experiments regardless of temperature variations ? Something is not in line in the story.

 

[DrDu]

Breaking a pair reduces the magnetic field which leads to an electric field which speeds up the other Cooper pairs which increase the magnetic field. In the end, the magnetic field stays constant and the cooper pairs speed up so as to keep current constant, as claimed by the London equations

 

[Stanislav]

Electromotive force occurs when the actual supercurrent really decreases anyhow. The contradiction is that the observed supercurrent doesn't decrease, so any EMF is absent. Moreover, annihilated superfluid carriers become normal and lose their momenta on lattice atoms, so the momentum conservation law requires that the supercurrent loses the momenta of annihilated pairs. So the supercurrent must actually decrease. However, it is never observed.