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I've seen this answer, which clarifies that superconductors float on top of permanent magnets not because of the Meissner effect, but because of flux pinning. The superconductor is cooled, and in that process discrete flux centers are created (thin lines of non-superconducting regions). Sometimes a hand-wavy explanation is provided which sound like "and therefore it cannot move because that would change the flux through the flux centers."

But it remains unclear to me why flux pinning prevents the superconductor from moving relative to the magnet. If the superconductor was moved far from the original magnet it cooled near, the superconductor would just make a current that preserves the flux through each of the flux centers. This is more in line with my experience with superconductors. I worked in a lab with superconducting magnets, and the primary observation was that when you tried to change the flux through a closed superconducting loop (like by turning off another magnet), the current in the superconductor would change to preserve the flux. Presumably this occurred only because our superconductors were held in place very strongly.

It seems this kind of argument can explain why it is possible to move a superconductor with a sufficient external force... and somehow gravity is typically not sufficient. In this video the person grabs the superconductor and moves it, and it stays in the new position. (By the way, it's not clear to me why the superconductor in the video can spin, but I'm not asking that right now.)

So what are the details of this argument? What prevents superconducting material from moving when it forms near an external magnet? What happens to the superconductor when you force it to move with a sufficient external force, and what sets the scale of that sufficient external force.

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    $\begingroup$ Writing this as a comment first to make sure I grasp your good question. Flux pinning is mainly associated with defects in the superconductor where the normal state has some energetic reason to preferentially occur (smaller superconducting gap, say). So flux lines tend to follow those defects. When you move the SC within the (inhomogeneous) B-field those lines tend to jump between defects, see this nice video m.youtube.com/watch?v=1kKMoQZ1JKo $\endgroup$
    – KF Gauss
    Commented Sep 8, 2023 at 11:55
  • $\begingroup$ @KFGauss Thanks for the comment. I was not previously aware that was the cause of flux pinning. I had (incorrectly i guess) assumed that as the phase transition proceeds, the magnetic field flux gets concentrated to one point, and that point has too high magnetic field to become superconducting (the superconducting phase transition goes down in temperature when $B$ goes up). So if your description leads to an answer to the question it would be very helpful. $\endgroup$
    – AXensen
    Commented Sep 8, 2023 at 12:00
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    $\begingroup$ There is a separate effect associated with $H_{c2}$ which is associated with the onset of flux vortices but is distinct from flux pinning because it occurs even in the absence of defects. The fields needed to reach $H_{c2}$ are usually many Tesla and far above permanent magnets usually used in demonstrations. I'll try to write this up $\endgroup$
    – KF Gauss
    Commented Sep 8, 2023 at 14:24
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    $\begingroup$ im curious about the answer here as well $\endgroup$ Commented Dec 14, 2023 at 4:39
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    $\begingroup$ If flux lines can only follow defects does that mean that wider gaps between defects could result in stronger flux pinning? Could someone introduce defects to a type 1 superconductor to make it participate in flux pinning as well? $\endgroup$ Commented Dec 14, 2023 at 4:40

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