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6

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 ...


3

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 ...


2

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 ...


2

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 ...


1

Someone might give a more precise answer in terms of group theory but I'll give it a go anyway ; feel free to edit my post. Instead of considering the case of an odd number of fermions, one can consider just a single spin $1/2$ - fermion to discuss $2 \pi$ rotations. Spin $1/2$ is a representation of dimension 2 of the rotation group, which is called the ...


1

Your confusion confused me at first too, but I believe I can help with the main point. Your mistake comes in the phase "picture of a Cooper pair being broken into two quasiparticles." A Cooper pair does not break into two quasiparticles. Just so we're on the same page, the BCS ground state is: $$\prod_k \left(u_k+v_ka^\dagger_{k \uparrow}a^\dagger_{-k \...


1

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.


1

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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