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I have been doing some reading on the formulation of BCS superconductivity. From what I understand, an additional non-vanishing term $\Delta c_{\uparrow,k}c_{\downarrow,-k} + c.c$ develops below the critical temperature resulting in electrons pairing up as Cooper pairs. What is however not clear to me how this results in a macroscopic quantum phenomena. Is the macroscopic nature due to pairing of electrons with positive and negative momenta and that that there are multitude of such states around Fermi level that satisfy the criterion that the net momentum of the pair be zero ?

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In a BEC, a large number of bosons occupy the same quantum state, at which point microscopic phenomena, like wavefunction interference, becomes appearant macroscopically.

An arbitrarily small attraction between the electrons causes the Cooper pair to have lower energy then the fermi energy, which implies they are bound.

One of the electrons is repelled from other electrons due to their negative charge, but it attracts ions that make up the rigid lattice of the metal. This distorts the lattice, moving the ions towards the electron. The ion charge density increases near the electron, and will attract other electrons.

At long distances (hundreds of nanometres), this attraction between the electrons (due to displaced ions) overcomes the EM repulsion, and cause them to pair up.

The trick is, that the electrons in the pair can be far away, hundreds of nanometres apart, since this interaction is long range. This distance is greater then the average inter electron distance, so many cooper pairs can occupy the same space. Cooper pairs are composite bosons, they are allowed to be in the same quantum state. The answer to your question is that this distance causes the microscopic phenomenon to become a macroscopic phenomenon, with the electrons interacting with the collective movements of ions in the lattice.

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  • $\begingroup$ why the downvote? $\endgroup$ – Árpád Szendrei Oct 6 '19 at 15:49

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