Cooper pairing without quasiparticles

Superconductivity is the ultimate fate of a Fermi liquid at low temperatures. More broadly, superconductivity occurs in many systems where sharp Fermi liquid quasiparticles are absent and the nature of pairing in such incoherent systems thus raises an important problem. I will present work on a natural generalization of the Sachdev-Ye-Kitaev model to systems of interacting electrons and bosons, which demonstrates that both critical and fully incoherent electrons still undergo a superconducting transition. I will describe various properties of the resulting state, such as the possibility of a strongly coupled fluid of Cooper pairs below Tc. I will also describe pair breaking effects due to time-reversal symmetry breaking, leading to a theory that may be understood as a non-Fermi liquid counterpart of the Abrikosov-Gor'kov pair breaking theory by paramagnetic impurities in superconductors.