Are Cooper pairs "ghost" particles that can go through each other?

Question

I understand that two electrons are "linked" by a phonon when the temperature is sufficiently low. My question is, since Cooper pairs are bosons, do they interact with each other? For example, if two Cooper pairs move toward each other, can they pass through each other like photons? If not, will scattering break apart the two Cooper pairs? They are still charged, right? Thank you.

Answer 1

My question is, since Cooper pairs are bosons, do they interact with each other? For example, if two Cooper pairs move toward each other, can they pass through each other like photons?

This question gets into a weakness of the "particle" approach to quantum mechanics. As with electrons and nucleons, you can't really distinguish between "this" Cooper pair versus "that" Cooper pair. Instead, it becomes more parsimonious to model your system as having a "Cooper pair field," with some density of particle-like excitations.

Superconductivity occurs when many Cooper pairs "condense" into the same quantum-mechanical state. This only happens when you have, on average, more than one pair per de Broglie volume. In a superconductor, the Cooper pairs are always overlapping; that's what makes the magic work. We can estimate the typical momentum, $$ \begin{align} \frac{p^2}{2m}&≈kT\\ (pc)^2&≈kT\cdot 2mc^2\\ &≈(0.3\text{ meV})(1000\text{ keV})\quad\text{ (near 4 kelvin)}\\ pc&≈17\text{ eV}, \end{align}$$ and thence the wavelength $$ \begin{align} \lambda &=\frac{hc}{pc} \\&≈\frac{1240\text{ eV nm}}{17\text{ eV}} \\&≈70\text{ nm}. \end{align} $$ This order-of-magnitude estimate is useful even if there are some factors wrong. The typical density of conduction electrons is something like one per $(\rm few×0.1\,nm)^3$, so the Cooper pairs must substantially overlap even if only a tiny fraction of the conduction electrons fall into the superconducting state.

If scattering between pairs destroyed them, the condensate would be unstable by definition. Instead, you have a zero-temperature phenomenon where no (or negligibly few) excited states are accessible, so everybody lives in the ground state.

They are still charged, right?

Yes, both electrons have negative charge. But they live on a positively charged ion lattice, so your instincts about repulsion may decieve you.