Superconductivity is two "crystals" sliding within each other?

The Wikipedia page states that it is imperfections in the lattice of atoms which causes resistance in a normal metal.

https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

Phonons are a time-dependent distortion of the lattice.

In our previous, March 14, 2022 blog post we remarked that scattering of electrons in a perfectly ordered crystal might be negligible.

Thus, the problem of superconductivity is why phonons or zero-point fluctuations do not cause scattering of electrons at a low temperature.

Copper, silver, and gold are not superconductors even at zero kelvin. There is some residual resistivity. Could it be that zero-point fluctuations in those metals are able to scatter electrons?

Two crystals sliding within each other

Ordinary resistance comes from the interaction of electrons with phonons. An electron is an individual particle, but a phonon is a collective motion of the lattice of atoms.

Could it be a general property of lattices that they tend to interact through their defects or distortions (usually phonons) and not through their individual particles? Let us assume that.

Let us assume that the conducting electrons at a very low temperature form a highly ordered structure, some kind of a "crystal". As the cloud of the conducting electrons slides past the lattice of nuclei, then only the "defects" of the electron crystal and the lattice interact. That is, only the phonons in each interact. The interaction of phonons probably does not cause much friction between the electron crystal and the lattice?

A phonon of the lattice can be converted to a phonon in the electron crystal. Can that process take momentum away from the sliding electron crystal? How does a phonon "jump" to the other material?

An analogous setting is a block of glass moving in a photon gas. If the glass would reflect the photons, it would certainly lose momentum. But if it is transparent, then it does not lose.

We conclude that the electron crystal can slide through the lattice of atoms without friction. This may explain superconductivity. We must analyze this in more detail.

Copper, silver, and gold

Could it be that the lattice of these metals is very stiff? A stiff lattice reduces the amplitude of phonons, and reduces resistivity at high temperatures.

We speculated about a "crystal" of conducting electrons in the previous section. The crystal apparently needs phonons of the lattice to form - the isotope effect strongly suggests that. The phonons in a stiff lattice may have too small an effect to bind electrons into an ordered structure even at zero kelvin.

Conclusions

In BCS theory, electrons form Cooper pairs through an unknown attractive force which is mediated by phonons. BCS theory does not try to explain what is this force and why the pairs can move within the lattice of atoms without scattering from phonons and losing their momentum.

Our crystal-within-lattice model may explain these things, at least qualitatively. Instead of pairs of conducting electrons, phonons at a low temperature bind whole ordered structures, "crystals" of electrons. 

The Cooper pair may describe the interaction between two "adjacent" electrons in the crystal.

What are these ordered structures of electrons? They cannot consist of a static lattice of electrons. Electrons move at large speeds.

A crystal is a collective phenomenon where a large number of particles are tightly bound to each other. Then the interaction of a single particle with an outside disturbance has to be replaced with the interaction with a large collection of particles. The excitation of a crystal structure is often a phonon.