Superconductor in a hollow cylinder -- two different end states. Why?

[annaphys]

When a magnetic field is applied to a SC during cool down, the field goes through the hole of the hollow cylinder. When the cool down first takes place and then later a magnetic field is applied, the magnetic field does not go through the hole of the hollow cylinder but rather is expelled to the exterior of the cylinder. Why does this happen? Why is there a difference between the two?

 

[DrDu]

Inside the bulk of the superconductor, there can't be a magnetic field. So the field inside the hole get's trapped.
You can also show that the field can't have arbitrary values but gets quantized.

 

[annaphys]

Hi thanks for the comment. What do you mean it gets trapped and which state are you referring to?

 

[DrDu]

In the superconducting state, the magnetic flux through the loop cannot change. If there was a flux inside, before cooling down, it gets trapped, i.e. you can't change it any more when the loop has become superconducting.

 

[annaphys]

Ok that makes sense. And for the other case, i.e. when first cool down then magnetic field, what makes it that no flux goes through the hole? Is this simply because the hole is relatively small and the screening current on all sides pushes the magnetic field out of the hole? If we had a cylinder, with a meter wide hole, could we see flux going through it?

 

[DrDu]

Is this simply because the hole is relatively small and the screening current on all sides pushes the magnetic field out of the hole? If we had a cylinder, with a meter wide hole, could we see flux going through it?

Yes, this is principally the explanation. The magnetic field cannot be made arbitrary strong, as this will make superconductivity to break down (critical field stength). The reasoning is also not completely applicable to type II superconductors, as small flux packets can enter the superconductor (Superconductivity vanishes at the location of the flux lines).

 

[Vanadium 50]

the magnetic flux through the loop cannot change

This is the key to the asymmetry. Whatever the flux was before the transition is what you have after. If it was zero before, it';s zero after. If it was non-zero before, it's non-zero after.