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Beautiful (in my opinion) source in which higgs mechanism nature of superconducting phenomena is discussed, is Steven Weinberg's QFT Vol. 2, sec. 21.6. Topological nature of superconucting vortices is discussed in this section. Also, there is general discussion on topological configurations in QFT, with theoretical minimum, in Chapter 23.

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Let me explain @ACuriousMind 's answer with some verbiage. The short, regrettably oracular, answer is that the Fabri-Picasso theorem does not hold in a finite superconductor, since translational invariance fails at its boundaries. Really, I do appreciate this is aggressively obscure: will strive to explain. First of all, if you have a chunk of warm ...

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In a superconductor, the electric resistance is equal to zero. This is why an electric current can circulate forever in a superconducting ring even when the battery has been unplugged! This is how magnetic fields are created in MRIs. Source:- http://www.supraconductivite.fr/en/index.php?p=supra-resistance-supra

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As you pointed out, the phonon-mediated BCS-type superconductors exhibit a gap $\Delta_0$ which is isotropic in $k$-space, we call it an s-wave gap. As @leongz pointed out, it comes from the fact that the electron-phonon interaction used in the BCS model does not depend a momentum ; inserting it into the gap equation gives a s-wave gap. The precise ...

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The temperature in space is not as easy thing, because it is not clear, what is actually whose temperature we want to know. On the Earth, the temperature in the meteorology means the temperature of the air in shadow. But there is no air in the space. The cosmical microwave background has a temperature of around 2.7K, but it is -270C and not -246C. But in ...

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These schemes have been proposed and studied. A spacecraft with a magnetic field could steer charged particles away from it. The magnetic field would have to be much stronger than the Earth's magnetic field. The reason is pretty easy to see. The Lorentz for $\vec F~=~q\vec v\times\vec B$ for the charged particle velocity perpendicular to the magnetic field ...

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In a superconductor, there is a one-particle gap but no two-particle gap. In a true insulator, all n-particle gaps are finite. With a small electric field you can still create gapless two-particle states in a superconductor, which carry a current. This current is non-dissipative because all particles are in a single macroscopic coherent state (the ground ...

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The difference is that in a normal conductor the current is carried by fermions (i.e. electrons) while in a superconductor the current is carried by bosons (i.e. Cooper pairs). Have a read through my answer to What is it about the "conduction band" of a material that is distinct from the valence band? where I explain why a full energy band cannot ...

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Normally Fermi energy is temperature dependent. We define the Fermi level at absolute zero. An insulator at temperatures near absolute zero have very less energy compared to the conduction energies. A superconductor state holds good at very low temperatures (liquid He temperature). The superconducting state is characterized by cooper-pair, which is not to be ...

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Existence of a gap means that ground state and excited states are well separated and a transition from ground state and excited states requires some energy. Existence of a gap does not determine whether a system is insulating or not. In your case, conductivity is determined by the ground state. For an insulator, the ground state is insulating while ground ...

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This is fully contained in the paper, from understanding the sections that came before your statement. Namely: Section 5 of the paper studies QED using "perturbative expansion" which requires the charge $e$ of the electron to be small, and this is how the Higgs mechanism (with respect to electrons) occurs. From Dirac's quantization condition, the charge $q$...

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