Grurgle-the-Grey wrote:SCs will Josephson couple only to other SCs over distances ~10nm, scanning tunnelling microscopes work at a range of .5nm.
Schroedinger does apply for the STM which works happily on an active super-conductor with NO Josephson current.
"Tunneling" between two superconductors is totally different from "tunneling" from a superconductor to a normal conductor. Note that In the latter you need a much higher voltage and what you extract are "normal" electronic charge- carriers which can "tunnel" over much larger distances. This is well known in the literature. Note the use of " " since the wave entities cannot really
tunnel through a barrier: This is impossible since it would violate energy conservation. What happens is that a "quantum fluctuation" supplies energy for a short time interval (delta)t which allows the wave-entity to scale the barrier with a speed v. Let is call the latter process rather "quantum-hopping".
So the entity that Josephson couples cannot be an electron, or a pair of electrons since they obey Schroe's equation and the SC entity doesn't.
Charge-carriers within a material
are never the same as "free" electrons outside the material. In a normal conductor, the charge-carriers are
wave packets which form by the superposition of de-localized electron waves which, when they do not superpose to form wave packets, are each present everywhere within the conductor. In a superconductor the charge-carriers are are localized stationary wave-entities, which move from one position to the next by quantum-hopping over the barriers which hold them otherwise stationary.
So if one wants to try and say that super-conductivity is caused by electrons the first thing to understand is why a fundamental particle can suddenly decide to ignore its Hamiltonian.
No conductivity is caused by electrons but by localized wave-entities caused by the superposition of electron-waves which, if they do not superpose would otherwise each fill then whole material. In a normal conductor these wave-entities are wave-packets, and in a superconductor they are localized, anchored orbitals that move by means of quantum-hopping.