# BCS theory of superconductivity and eternal supercurrents?

• A
• StanislavD
In summary, the Cooper pair density depends on temperature, meaning that pairs can be created/annihilated by temperature variations. However, 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.
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?

StanislavD said:
How to solve the contradiction of theory/experiment?
With math. Calculate how long you expect the supercurrent to persist and compare with data.

hutchphd and Lord Jestocost
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.

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.

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.

StanislavD said:
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.

berkeman
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.

weirdoguy

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

StanislavD and hutchphd

## 1. What is the BCS theory of superconductivity?

The BCS theory of superconductivity, also known as the Bardeen-Cooper-Schrieffer theory, explains the phenomenon of superconductivity in certain materials at low temperatures. It was developed in 1957 by John Bardeen, Leon Cooper, and John Schrieffer and is considered to be one of the most successful theories in modern physics.

## 2. How does the BCS theory explain superconductivity?

The BCS theory proposes that at low temperatures, electrons in a superconductor form pairs called Cooper pairs, which can move through the material without any resistance. This is due to the attractive force between the electrons caused by the vibrations of the crystal lattice. These Cooper pairs are able to move through the material as a supercurrent, allowing for the zero resistance and perfect conductivity observed in superconductors.

## 3. What is the role of phonons in the BCS theory?

Phonons, which are vibrations of the crystal lattice, play a crucial role in the BCS theory. They are responsible for the attractive force between electrons, which allows them to form Cooper pairs and move through the material without resistance. Without phonons, the BCS theory would not be able to explain superconductivity.

## 4. Can the BCS theory explain all types of superconductors?

No, the BCS theory can only explain superconductivity in conventional superconductors, which are materials that exhibit superconductivity at low temperatures. It cannot explain high-temperature superconductors, which have a different mechanism for superconductivity that is still not fully understood.

## 5. What is the significance of the BCS theory in modern physics?

The BCS theory is significant in modern physics because it provided the first successful explanation for superconductivity and has been confirmed by numerous experiments. It also led to the discovery of new materials with superconducting properties, which have important practical applications in fields such as electronics, energy, and transportation.

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