Hi just completed a chapter on Superconductivity in a solid-state physics book. I have a few remaining questions. I don't expect they can be easily answered, but I appreciate if someone happens to know. Most of the questions regard how the equations have been motivated. I guess that's kind of nitpicky but I like to understand the history of it.(adsbygoogle = window.adsbygoogle || []).push({});

(1) In the Cooper pair interaction, why is the el-el interaction ignored for all el- states with energies much greater than the typical phonon (where el- energy is measured relative to the Fermi level). I understand two el- states whose energy difference is greater than a typical phonon won't interact directly. But that doesn't make a statement about their absolute energies. Would I be right to say this is because we don't expect the bound Cooper state to contain these states in the solution and so it's mathematically simpler to just zero the potential for the interaction out at higher energies?

(2) Is there a better way to motivate the BCS variational form? This form is Prod[ uk + vk c_(-k)* c_k ]|0> in standard notation. Since a Cooper pair is actually linear superposition of c_(-k)*c_k states, this doesn't quite match as a "filling of Cooper pairs." Can the BCS form be derived from a Slater determinant of Cooper pairs? Perhaps all of them in the same eigenstate (since they colloquially behave like bosons).

(3) The most characteristic property of a superconductor is the zero resistance. The explanation of this is that "Changing the momentum of a single pair with respect to the common momentum requires a cost in energy equal to the binding energy. As soon as the number of pairs with random momenta increases, the energy penalty to sustain the situation becomes prohibitively large: any scattering process, that occasionally breaks or restores Cooper pairs, tends torestorethe situation in which the pairs have common momentum." Is this supposed to be obvious? I just don't see why it becomes increasingly hard to break Cooper pairs as you continue to break them. The first one to break cost the binding energy. Why not also the last one?

(4) In Ginzburg-Lindau, is psi supposed to represent the wave-function of a Cooper pair (as in all Cooper pairs condense into the same state)? If not, where did they come up with the idea of a |(p-eA)psi|^2 term in the free energy?

(5) In the Josephson effect, why do begin with the assumption that the order parameter is constant in the superconductor and decays in the insulator? Isn't it the other way around when we consider the Meissner effect (i.e. boundary condition psi = 0 at surface and rises to bulk value in superconductor).

Thanks,

Sam

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# Theory questions on superconductivity

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