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  • $\begingroup$ @JeffreyJWeimer It looks like the whole Fermi sphere is shifted by a tiny bit when we apply an E field, but it isn't so (as Ziman puts it, it is misleading). Due to Pauli exclusion principle, the E field only affects the electrons going in the E field's direction and change their momentum's direction against the E field. About less than 1 in ten billions free electrons are able to do so. I can give you several references if you want. $\endgroup$
    – untreated_paramediensis_karnik
    Commented May 30, 2019 at 12:40
  • $\begingroup$ @JeffreyJWeimer I would, as I wrote in my post already, look at $E_F$ plus and minus an energy range that's proportional to $|\vec E|$. The math is done in Datta's textbook (available with google as a browsable PDF), page 39. $\endgroup$
    – untreated_paramediensis_karnik
    Commented May 30, 2019 at 12:49
  • $\begingroup$ @JeffreyJWeimer it isn't affecting the shape of the sphere. Again, that's an incredible small perturbation, the shift is insanely small (look at the numbers I wrote in my post). So I am not sure where you're leading me at. On a sketch it looks like as if the whole Fermi sphere had shifted, but physically this is not what happens. I do not see how this helps answering the question. $\endgroup$
    – untreated_paramediensis_karnik
    Commented May 30, 2019 at 12:51
  • $\begingroup$ @JeffreyJWeimer I do not see how it is possible, due to Pauli's exclusion principle. When the energy of interaction is not high enough for the low energetic electrons to go to higher non occupied states, they cannot interact. That's how superconductivity work, in a way. Here an applied field is a very small perturbation which cannot excite almost any of the free electrons. And there aren't 10 billions of them. I said that the E field can change the momentum of about 1 per 10 billion of them, that's quite different... but anyway how does this help answering the question?! $\endgroup$
    – untreated_paramediensis_karnik
    Commented May 30, 2019 at 13:01
  • $\begingroup$ Ashcroft and Mermin discuss this in their Chapter 13, the Semiclassical Theory of Conduction in Metals. Following a volume of electrons as they move through phase space, their ends up being a factor of the derivative of the Fermi function with energy which is non-zero only within a few kT of the Fermi energy. $\endgroup$
    – Jon Custer
    Commented May 30, 2019 at 13:14