From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. 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 decreases. However, this supercurrent decrease is never observed. Does it mean that the superfluid density is independent of temperature ?
Putting in simple words, in a superconducting ring with a persistent supercurrent, the supercurrent is maintained by the magnetic flux quantization, not just the superfluid density ~this is where the apparent paradox arises.
Thank you for the answer. But it generates a new question. The flux is quantized, some pairs are annihilated in the BCS. The flux is constant, then the annihilation of some pairs does acceleration for remaining pairs (and the pair creation slows down the remaining pairs). What is the force doing that ?
A massive ring may contain a huge number of flux quanta. Why BCS doesn't allow that the flux also decreases quantum by quantum together with pair annihilation ?
Another question. A pair is annihilated, 2 electrons become normal. This means the supercurrent momenta of the 2 electrons dissipates on atom lattice. The momentum conservation law requires that the supercurrent loses the momenta of the 2 lost electrons. Thus, does the pair annihilation violate the momentum conservation law?
Dear Stanislav,
Do you guess that the pairs velocity doesn't depends on temperature?
Maybe the pair velocity depends on temperature, I don't know. However, the supercurrent momenta of annihilated pairs are lost on the lattice, and the momentum conservation law requires that the supercurrent loses the momenta of annihilated pairs. I don't think the temperature can somehow accelirate remaining pairs exactly toward supercurrent direction
I meant that the superconductor tends to maintain
magnetic flux.
If the pairs concentration decreases, the current
can remain constant by increasing the pairs velocity. There is no loss of torque also.
Yes, the total momentum and angular momentum of supercurrent must be constant with increasing temperature (T). Then the flux is also constant. If some pairs annihilate, then their momenta must unavoidably dissipate on atom lattice. Thus, the pair annihilation and momentum conservation of the total current cannot be maintained at the same time. Moreover, just below Tc the pair density tends to zero, so the increasing T cannot provide the strong enough velocity increase for the compensation of lost momenta. Moreover, if remaining pairs take the thermal energy, then it means the pairs interact with thermal energy of lattice - this contradicts with the idea of dissipationless movement of superfluid density. These simple considerations hint that the pair annihilation doesn't take place in superconductors. Then everything is well explainable, the pair density is constant, the pair velocity is constant, the current and flux are constant.
A simple argument for why the external thermal energy cannot compensate the lost angular momentum of supercurrent. External thermal energy (which heats the superconductor) has no angular momentum. Thus the thermal compensation of the angular momentum (which is lost due to pair annihilation) would violate the conservation law of angular momentum.
PS. Many thanks for your answers and doubts. Now the picture of superconductivity is more clear than before our discussion
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