How do Cooper pairs carry a current with zero net-momentum?

[alberliu]

TL;DR Summary

How do Cooper pairs carry a current with zero net-momentum?

One of the first starting points of introducing BCS theory in a superconductor is applying a theorem stating that the ground-state of a quantum system has an expectation value for its momentum of zero. You then use this to say that an electron must pair with another electron of equal and opposite momentum to form a Cooper pair.

If this is the case, how does this zero-momentum state result in a finite supercurrent? Maybe this is a frame-of-reference issue, but it's not clear to me how you get net charge movement in one direction with a net momentum of zero.

 

[DrDu]

That's simply not true. In a state with finite current, the Cooper pairs don't have finite momentum and the electrons in a pair don't have exactly opposite momentum. In the book by Schrieffer "Theory of superconductivity", this is explained in detail.

 

[bbbl67]

Summary:: How do Cooper pairs carry a current with zero net-momentum?

One of the first starting points of introducing BCS theory in a superconductor is applying a theorem stating that the ground-state of a quantum system has an expectation value for its momentum of zero. You then use this to say that an electron must pair with another electron of equal and opposite momentum to form a Cooper pair.

If this is the case, how does this zero-momentum state result in a finite supercurrent? Maybe this is a frame-of-reference issue, but it's not clear to me how you get net charge movement in one direction with a net momentum of zero.

I think you've mistaken electron spin with linear momentum. The Cooper pairs are of electrons with opposite spins, not opposite momenta. Now, the electrons will be very close to absolute zero, so their linear momenta will be very close to zero as well, but it's not a requirement that they stay at zero momentum once they've already paired up.

Electricity is actually a very slow movement of electrons in non-superconductive situations, but in superconductive situations, it's likely just as slow if not slower, but it's not the individual electron speeds that matter but the overall movement of a mass of electrons that give you your power.