The conceptual model I have been introduced to for cooper pairs in a bulk superconductor is what I would call the "wake" model, where one electron deforms the positively charged lattice, changing the potential energy landscape and causing the second electron to be drawn closer.
This seems like a terrible conceptual picture both because the electrons in a superconductor should have a well defined localized wave function and because the ground state of the BCS theory has zero net momentum, which would suggest they orbit around each other or something...
If anyone can explain how I should be thinking about this I would be very grateful.