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I'm studying superconductivity and BCS theory. Looking at the BCS ground state construction, I see two things that seem conflicting

  • Occupation of Cooper pairs in BCS ground state (look at the figure below from Ibach)
  • The fact that the only electrons in the region $\pm \Delta$ about $E_F$ contribute to BCS ground state

So where did other electron (electrons not in the $\pm \Delta$ region) go?

enter image description here

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So where did other electron (electrons not in the $\pm \Delta$ region) go?

They are just there as regular Fermi gas that don't really feel the phonon interactions that trigger the Cooper pairs because their energy scale is "too different" from the magnitude of the interactions so they are pretty much not scattered/disturbed by the interactions.

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