BCS Theory of Superconductivity

Question

I'm currently taking an introduction to Solid State Physics class, and is now on the subject of superconductivity (SC). Currently I'm reading about the BCS theory, and how this works on a microscopic scale. I then get presented with this picture (Electron-Phonon Interaction):

Now, as far as I have understood, the electrons, when below $T_{C}$, attract the ions, but are too fast compared to the ions, which means that the ions contract after the electron is gone. This creates a higher potential in the area where they are "squeezed" together which the next electron is much more attracted to that usually. This again means that all electrons pretty much follow the same path, and somehow bond together in Cooper Pairs (Is this the way they get entangled?).

Now, my main question is: Does this attraction of ions, after an electron has moved past them, not happen to a normal metal ? I mean, the electrons move in a normal metal, and also past ions. So don't they attract the ions as well, and make this attraction that another electron then can follow as well ?

Answer 1

The attraction does happen at all temperature, but it is negligible if the temperature is too high. So the electrons do attract each other, but the thermal fluctuations do not allow for Cooper pairs to be stable.

To give an heuristic example : Imagine a lot of hydrogen atoms. The electrons are bound to their protons at zero temperature. If now you put the hydrogen atoms in a medium with a temperature high compare to 13eV (the binding energy), the electrons can take some energy from environment to leave their protons, and you don't have hydrogen atoms anymore, but a plasma (free protons and free electrons, interacting without forming bound states). The same thing happens with Cooper pairs : the temperature needs to be small enough to allow the physics to be dominated by these very weakly bounded pairs.

Answer 2

Don't forget the direct repulsion between electrons due to Coulomb force. From the point of view of renormalization group theory, temperature effectively change the magnitude of the attraction by the ions and the Coulomb repulsion. When temperature is low enough, the attraction is larger than the repulsion, then Cooper pairs form.