A charge-4e superconductor forms due to the condensation of quartets of electrons. While in previous works the mechanism for the formation of charge-4e superconductivity has been analyzed in terms of the binding of Cooper pairs in unconventional superconductors, its properties in the fermionic sector have not been studied systematically due to its inherently interacting nature even at the mean-field level. Here we propose a solvable model for a charge-4e superconductor – a spinful version of the Sachdev-Ye-Kitaev model with an anomalous quartic term. We present results on the Luttinger relation, superfluid density, and low-temperature instabilities for a charge-4e superconductor in the weak and strong-coupling limits, and show that they are in sharp contrast with a conventional charge-2e superconductor.
