I'm interested in reading an explanation of superconductivity, but though I have an undergraduate degree in engineering, I'm not sure I'm up to reading a detailed mathematical treatment of the theory. Still, I'm willing to give it a shot. Can anyone suggest the clearest overview of how superconductivity works, both with as a technical paper and a lay explanation if available?
Superconductivity is easiest to understand when it is point bosons that do the superconducting. This theory is just the theory of a charged superfluid, and it was worked out by Landau in the 1950s. The model plus the calculation of the magnetic screening length appears on Wikipedia page for "Higgs Mechanism".
In elemental metals, the bosons are weakly paired electrons, so that the bosons are emergent and composite, and their scale of compositeness is very large compared to the atomic spacing. This makes the analysis more difficult, because it requires perturbing a Fermi surface. But the main gist of the effect, the phenomenology, is all contained in the point-boson model.