What makes cooper pairs hop to another superconductor? I know the derivation and how the Josephson effect works. But if we just have two slabs of superconducting material placed together with an insulator between them, what makes the initial hopping occur? There has to be some potential difference somewhere right? Just because they can hop doesn't explain what initiates the hopping. Or does this hopping just occur randomly more times over? I know there is a macroscopic wave that defines the total cooper pairs in each slab, but it is simply the phase difference between the two waves that causes the hopping? That means if the two wave functions are orthogonal to each other, we wont see any hopping?
 A: Hopping is a bad way to understand the physics of superconductors, because it implies movement of discrete charges, whereas the state of a superconductor has a definite phase and uncertain number of Cooper pairs, which do not commute and therefore related via the uncertainty relation:
$$[\varphi, N]=i.$$
In other words, the number of charges on a superconducting island fluctuates, and its wave function is spread beyond the superconductor island itself, on what is known as the proximity effect. Moreover, constraining the number of charges in a superconducting island (e.g., in small droplets, via Coulomb effects) is known to kill the superconductivity.
The emergence of hopping thus can be viewed in (at least) two different ways:

*

*when the two slabs of superconductor material are brought close to each other (i.e., closer than the coherence length of the proximity effect)

*when the two nearby slabs are cooled into the superconducting state, in which case the "hopping" emerges as the result of the diverging charge fluctuations near the phase transition.

