Before trying to understand charge imbalance in superconductors (eg Hübler et al., Phys. Rev. B 81, 184524, Quay et al., Nature Physics 9,84–88 (2013)) I thought I had better check I understand the equilibrium situation, and I now realise that I don't.
In particular, I don't really understand quasiparticles. Apparently they are a superposition of electron and hole. Here is the usual sort of diagram;
showing (above) the anticrossing opening up between electron and hole branches in the superconducting phase and (below) the Bogoliubov amplitudes, giving the amount of hole like or electron like character of the quasiparticle. So it seems to me that quasiparticles at the band edge (energy of $\Delta$) must always be neutral, as they are equal parts hole and electron. But this does not sit very well with my picture of a Cooper pair being broken into two quasiparticles by a photon of energy $2\Delta$. Such a photon would (or could) create two quasiparticles at the band edge, which therefore have total charge zero, starting from a Cooper pair of charge $2e$. What's gone wrong here?
I also have trouble reconciling this with my understanding of superconducting single electron transistors (SSETs). Here's a figure from this paper, showing gapped Coulomb diamonds in an SSET;
There's a lot going on here, but the relevant thing for this question is that quasiparticles are being injected at the band edge, where (again) they should have zero charge, but they are still capable of contributing to the conductance. Something is very wrong with one (or both!) of my understandings.
(There is already a related question here but it didn't get an answer.)
Edited to add:
I found this paper, which describes QPs as rotons in the Cooper pair sea, with spin but no charge. The charge is perfectly screened, and so lives at the surface somewhere. I'm not sure it clarifies things much.