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.

 

[DrDu]

There is no momentum conservation for the electrons alone. Momentum can always be taken up from or given to the lattice.

 

[Stanislav]

Do you think the lattice takes the momentum of annihilated pairs and gives it to the living pairs ? How can the lattice know the direction and particles to be accelerated ? Why cannot the lattice boost normal electrons ? Too magic. Rather, the pair density is independent of temperature.

 

[Stanislav]

Moreover, if the lattice takes the momenta of pairs, it takes also their energy. But the energy of atoms with the momenta of pairs is much lower than the energy of pairs with the same momenta, because the atoms are much heavier (if mv=MV, then mv^2 >> MV^2). Thus, some energy of dissipated pair momenta vanishes (probably as heat and radiation) and lattice cannot recover the lost momentum of pairs because of the energy deficit.

 

[Stanislav]

Thermal energy cannot recover the lost pair momentum because the thermal energy cannot spontaneously be converted into ordered momentum.

 

[DrDu]

In principle, this is the Einstein - de Haas effect. The electronic sub-system condenses into a broken symmetry state with non-vanishing angular momentum and the complete system starts to rotate due to angular momentum conservation.

PS: Obviously, I am not the first one to remark this connection: https://journals.aps.org/pr/abstract/10.1103/PhysRev.86.905

 

[Stanislav]

Exactly. The angular momentum conservation works in superconductors at warming. Annihilated pairs give their momentum to lattice, and then the supercurrent momentum must decrease. However, the supercurrent remains constant. Conclusion: the pairs don't annihilate at warming.

 

[DrDu]

Found this interesting article: https://arxiv.org/pdf/1609.08451

 

[Stanislav]

Yes, thank you. Professor Hirsch also noted that generally accepted theories are contradictory.

 

[DrDu]

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.

I really think there is a very small transient decrease of supercurrent, if you suddenly decrease the superconducting density by changing the temperature. The penetration depth of the magnetic field and of the current density is proportional to 1/sqrt(n_s). A decrease in n_s leads to an increase in magnetic field and this goes in hand with an electric field. The change will never be instantaneous, as the newly generated normal conducting electrons need time to loose their current in collisions with the lattice. The electric field will be small but it must exist, simply because the electric field and acceleration are simultaneous, but velocity lags behind. The electric field acts both on the superconducting electrons and on the positively charged lattice, so momentum is automatically conserved.