BCS theory of superconductivity and eternal supercurrents?

[StanislavD]

TL;DR Summary

The BCS theory of superconductivity assumes creation and annihilation of Cooper pairs due to temperature fluctuations below Tc. This recombination process should unavoidably destroy an initial supercurrent. However, in experiments the supercurrent is insensitive to temperature fluctuations and exists forever. How to solve the contradiction of theory/experiment?

In the BCS theory the Cooper pair density depends on temperature, meaning that pairs can be created/annihilated by temperature variations. Obviously, momenta of annihilated pairs dissipate on the atom lattice, so an initial supercurrent dissipates. On the other hand, in some experiments a supercurrent, once excited, runs for many years despite any temperature fluctuations below Tc, indicating that any pair annihilation doesn’t take place. How to solve the contradiction of theory/experiment?

 

[Vanadium 50]

How to solve the contradiction of theory/experiment?

With math. Calculate how long you expect the supercurrent to persist and compare with data.

 

[StanislavD]

The solution is available. In BCS the supercurrent must somehow decrease because of thermal fluctuations (slowly or fast – depends on cryostat quality, however it is about microseconds, not about hours). In experiments – the supercurrent is constant for years, probably forever, independent of any thermal variations (even macroscopically large ones). This fact doesn't need a further math.

 

[Vanadium 50]

I find this hard to believe. I certainly would have preferred a calculation to a description of 1.

Consider mercury in liquid helium - and I am doing myself no favors by picking this pair, as opposed to say, niobium. Tc = 4.2K and T=4.15K. Temperature fluctuations are of order T/√N where N is the number of participants: around Avagadro's number. So you have sub-nanokelvin level fluctuations. It takes a billion standard deviation excursion for thermal fluctuations to cross Tc.

I don't see microseconds as having enough time to have an excursion this large.

 

[StanislavD]

Another experiment. We vary T of mercury up/down, say from 3K to 2K and back. A supercurrent is excited before the first T-circle. According to BCS every T-circle destroys a not negligible fraction of pairs at warming, and creates the same fraction of pairs at cooling. The electromotive-force (EMF) is no longer available, so broken pairs lose the supercurrent momentum; newly created pairs did not experience any EMF. Hence, the supercurrent must decrease at every T-circle. However, never observed the supercurrent decreases below Tc. Thus, the pair recombination (assumed in BCS) is not available.

 

[Vanadium 50]

Another experiment

This isn't an experiment. But anyway, the game of you make an undefended claim and I shoot it down and then we do it again is more fun for you than for me.

 

[StanislavD]

Unfortunately, it is not fun for me. Since years nobody could explain me the paradox of recombining pairs in the supercurrent. And few people recognize the issue as a real theoretical default of conventional theories; too uncomfortable situation for renowned institutions.

 

[berkeman]

Thread closed temporarily for Moderation...

 

[berkeman]

Thread will remain closed; the question has been asked and answered.

Also, here is a helpful PM that was sent to me to pass on to the OP:

"The ability of a superconductor to carry a dissipationless current, that is, a current under zero applied voltage, disappears if the superconductor is shaped into a thin cylinder or a thin wire, or, in other words, if the superconductor is quasi-onedimensional (see Figure 1.1). This is because if the diameter of the superconductor is small, the rate of strong thermal fluctuations, which bring short segments of the wire into the normal state, is essentially greater than zero at finite temperatures.

Such fluctuations, first predicted by William Little in 1967 [17] and called Little’s phase slips (LPS), occur stochastically at random spots on a superconducting wire and interrupt the dissipationless flow of the condensate."

From: Superconductivity in Nanowires: Fabrication and Quantum Transport by Alexey Bezryadin