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I don't have a definitive historical answer, but here are some pointers.
The idea of using order parameters to describe symmetry-breaking phase transitions (in particular second-order or continuous phase transitions) is due to Landau and dates back to 1937. His central observation was that a symmetry is either broken or not, and that if the phase transition ...
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Essentially, there is nothing special about the lattice of a semiconductor that would prevent it to "host" Cooper pairs.
The process that you describe of "pairing all electrons before entering [your preferred material here]" is called proximity effect. You just juxtapose a superconductor with another material (generally a non-...
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You are correct. There is a $c$-number energy shift:
$$
\hat H_{\rm Bogoliubov}= a^\dagger_i H_{ij}a_j +\frac 12 \Delta_{ij} a^\dagger_i a^\dagger_j +\frac 12 \Delta^{\dagger}_{ij} a_i a_j\\
= \frac12 \left(\matrix{ a^\dagger _i &a_i}\right)\left(\matrix{ H_{ij}& \phantom {-}\Delta_{ij}\cr
...
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Hopping is a bad way to understand the physics of superconductors, because it implies movement of descrete charges, whereas the state of a superconductor has a definite phase and uncertain number of Cooper pairs, which do not commute and therefore related via the uncertainty relation:
$$[\varphi, N]=i.$$
In other words, the number of charges on a ...
1
In a conventional conductor, the current density and the electric field obey Ohm's Law, $\vec{J} = \sigma \vec{E}$. A perfect conductor, such as a superconductor, is the $\sigma \to \infty$ limit of this equation; this implies that in this limit, we must have $\vec{E} \to 0$ in order to have $\vec{J}$ approach a finite limit.
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