Experiments for temperature dependence of persistent supercurrent?

[StanislavD]

TL;DR

According to the BCS theory of superconductivity, the superfluid density decreases at warming. Hence an eternal supercurrent must also decrease. However, all observations indicate that the supercurent is stable although every cryostat produces temperature scattering. Does someone know papers about direct experiments for the temperature dependence of persistent supercurrents in superconductors?

Imagine, in a mercury ring (superconductivity below Tc=4.15 K) we establish a persistent supercurrent. Then we organize temperature cycles (T-cycles) in the cryostat, from 3 K to 2.5 K and back. According to the BCS theory of superconductivity, the pair density decreases at warming, i.e. a not negligible fraction of pairs annihilates; the same fraction of pairs emerges back at cooling. Annihilated pairs lose their ordered supercurrent momentum on the atom lattice, so the supercurrent decreases at warming; newly created pairs do not experience any electromotive-force (EMF), since the EMF is no longer available in the ring. Hence, according to the BCS theory, the supercurrent must decrease at every T-cycle and dissipate after a number of T-cycles. However, in all experiments the supercurrent remains constant (despite large temperature variations in cryostats) and, thus, the pair recombination (assumed in BCS) doesn’t take place.
Do the pairs really annihilate when they flow in an eternal supercurrent?
Are there any papers about direct experiments with a supercurrent at different temperatures?

 

[Vanadium 50]

I don't think that's how it works.

If I have a current density j (j < j_c) and cool it, I still have a current density j. If I heat it (but not so much that j exceeds j_c) I still have a current density j. If I heat it further (so j > j_c) the current doesn't drop - the material goes normal.

 

[StanislavD]

Exactly. The case j < j_c is very interesting. If j is independent of temperature, then the superfluid density is also independent and, thus, we can verify an important BSC prediction.