Persistence of a knotted Abrikosov vortex

[Hornbein]

Suppose we have a Type II superconductor that contains a knotted Abrikosov vortex. How long can we expect this to persist? I read that the the core of the vortex is not superconducting, so energy would be dissipated. But how about the supercurrent? Once it got started, what would stop it? So I dunno.

 

[M Quack]

The core of a vortex is indeed not superconducting, that is why you can have a magnetic field in there.

This implies that there is also no supercurrent within the vortex.

Nevertheless, the non-SC state within the vortex has a higher energy than the SC state around it, so the system will try to minimize the volume fraction of vortex cores. Vortices either get pinned on defects where SC is weakened anyways (hence less energy lost), and loops, wiggles, etc in vortices get straightened out.

I don't know if and how you can tie a know into a vortex line (I'd appreciate if you could post an image of a bowline :-) ), but I suppose they would shrink and vanish unless strongly pinned.

If you draw a loop around a vortex - antivortex pair (magnetic field pointing up and down, resp.), then the net flux through this loop is zero and hence there is no net supercurrent around the pair. The currents around the two vortices compensate each other.