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I have a little conceptual doubt about the BCS theory of superconductivity. A visual model of the Cooper pair attraction has a passing electron which attracts the lattice, causing a slight ripple toward its path. Another electron passing in the opposite direction is attracted to that displacement. This constitutes a coupling between electrons. This coupling is accompanied by phonon interactions.
But the ripple in the lattice means the positive ions get slightly displaced towards the electrons. This is giving me a headache. The electrons are free to move. But ions, which are much heavier moves to the electron while the electron remains undisturbed throughout it's motion. But one should expect the opposite. Less massive electrons will move towards the positive ions. Could anyone tell me why this is happening?
Does it arise due to the repulsion of ions?

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    $\begingroup$ Please see our guide on writing good titles. $\endgroup$ – user10851 Apr 12 '16 at 2:39
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To buid up a bit on Tamasger's awnser, BCS can indeed be very non-intuite at first glance. The picture where the electrons locally disturbs the lattice and in return attract another electron is a good one to understand the basic concept of pairing, but is far from being able to capture all the physics.

Remember that phonons (the disturbance of the lattice) and electrons are quantum particles, and need to be treated as such. In particular, electrons are fermions : they are subject to the Pauli exclusion principle.

For the electron to be attracted to the lattice it would need to change its wavevector, but the available phase space to do this is very restricted because of all the other electrons that fill up the Fermi sea: its wavevector thus stay the same. This is not the case for phonons which are bosons, many of them can pile up in the same state.

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  • $\begingroup$ At absolute 0, if the electrons are indeed deforming the lattice (so the material is superconductor), would that mean that the entropy is non zero? Because for the entropy to be 0 in a perfect crystal, there shouldn't be any deformation from a perfectly regular lattice. And a non zero entropy for a crystal at 0K is problematic. Could you clear this up? $\endgroup$ – thermomagnetic condensed boson Aug 9 '18 at 9:14
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Your confusion arises because you take the "visual model" too seriously. According to BCS theory, there is a certain kind of electron-phonon interaction, which can be shown to be an effective attraction between two electrons (that need to be on the surface of the Fermi-sea). This coupling generates a binded state in the right conditions, and electrons stay in this state, so they can't loose energy. ,,This coupling is accompanied by phonon interactions." This is not right, the coupling is itself an electron-phonon interaction. The ,,ripples" of the lattice are what we describe by the phonon picture. Also, you wrote "The electrons are free to move.", but this is not the case. Electrons move in a potential that comes from the coulomb interaction of ions and other electrons. Rest assured, BCS theory is far from intuitive, so you cannot rely on metaphores.

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  • $\begingroup$ That's one good explanation but it's not getting out of my head $\endgroup$ – UKH Apr 10 '16 at 16:32
  • $\begingroup$ Since at absolute zero, there is no phonon, are you saying that superconductivity cannot exist at 0K? $\endgroup$ – thermomagnetic condensed boson Aug 9 '18 at 9:12

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