Understanding the Cooper pair in real space

[neuva]

I am trying to understand the pairing mechanism in the Cooper pair in real space. When I googled the image of the Cooper pair, there are two different pictures explaining the pairing. While one describe the second electron moving in the same direction, other describe it as moving along the same direction. Which one is correct? Does this answer depends on the pairing symmetry? s, p, d-wave?

Moreover, if the answer is that two electrons are moving in opposite direction, how can there be a net current? Thank you in advance.

 

[ZapperZ]

I am trying to understand the pairing mechanism in the Cooper pair in real space. When I googled the image of the Cooper pair, there are two different pictures explaining the pairing. While one describe the second electron moving in the same direction, other describe it as moving along the same direction. Which one is correct? Does this answer depends on the pairing symmetry? s, p, d-wave?

Moreover, if the answer is that two electrons are moving in opposite direction, how can there be a net current? Thank you in advance.

The cartoon picture is there to depict that, to preserve the fermion statistics, the 2 electrons that are in close proximity to each other have opposite momentum (k) states. This is true regardlesso of the pairing symmetry.

For the last part, this is more difficult to visualize. You need to know that electrons continue to scatter in and out of these states, i.e. you have no way of tracking which electrons are doing what. All you have in the description is that these Cooper Pair states are occupied. The super current is more of the result of long-range coherence of the condensate.

Also remember that in classical statistics, you can have a purely random scattering events and still have a net drift velocity in a particular direction of the whole ensemble. So looking at just one event or one pair, as in this case, will not give you the correct picture on the current transport.

Zz.

 

[DrDu]

They only move in opposite directions if the net current is zero. If the current is nonvanishing, the center of mass has a nonzero speed and the electrons only move in different directions with respect to the center of mass frame.