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Since superconductor is a conductor of electricity, the electric field of the electron should repel electrons in the superconductor, thus making the superconducor itself have an electric field that attracts the electron.

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The first thing you have to realize is that the superconducting state is the ground state of the system. In this scenario, the Cooper pairs of electrons are basic entities with some binding energy. The $2\Delta$ gap you mention doesn't refer to an excitation across the band gap of the material, but to to breaking of such Cooper pairs. This breaking of ...

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The full Maxwell equation $j=\nabla\times H+\partial_{t}D$ ($j$ current, $H$ magnetic field and $D$ electric induction) is recover from the action $$S=\int dx\left[L\left(A_{\mu}\right)\right]=\int dx\left[-\dfrac{F_{\mu\nu}F^{\mu\nu}}{4}-j_{\mu}A^{\mu}\right]$$ in a standard way, provided we define $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$ ...

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In short, what makes a superconductor topological is the nontrivial band structure of the Bogoliubov quasiparticles. Generally one can classify non-interacting gapped fermion systems based on single-particle band structure (as well as symmetry), and the result is the so-called ten-fold way/periodic table. The topological superconductivity mentioned in the ...

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A prototypical example of an intrinsic topological superconductor is the so-called $p$-wave superconductor [more details there: What is a $p_x + i p_y$ superconductor? Relation to topological superconductors, also, Meng-Cheng wrote the spinless $p$-wave model in 2D somewhere else on this page, and comment it carefully]. You can also induce topological ...

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I came across this opinion that whenever there is an instance of inhomogenous magnetisation, there is a split in ZFC and FC. In case there is a uniform long range ordering present, the ZFC will fall perfectly on the FC. Does any one have any insights on this view?

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This is the relation between the scattering matrix and the Green's function (notice that $(H_M-E-i\pi WW^\dagger)^{-1}$ is basically the Green's function, where $i\pi WW^\dagger$ is the self-energy correction due to coupling to the leads). For a pedagogical account, a good reference is Datta's "Electronic transport in mesoscopic systems", which is in general ...

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A zero-field-cooled/field-cooled split in the magnetic susceptibility vs. temperature doesn't have to be superparamagnetism. In the case of superconductors, if we apply a field to the material and cool past T$_c$, some flux can be trapped inside, but if we cool first and then apply field, that flux will be shielded away, resulting in greater diamagnetism.

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