Solvable model for a charge-4e superconductor

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. We propose a solvable model for a charge-4e superconductor -- a spinful version of the Sachdev-Ye-Kitaev model with an extra quartic anomalous term. Despite explicit violation of particle number conservation, the model remains gapless and satisfies Luttinger's theorem. We analytically solve for the superfluid density and show that it is perturbative in the strength of the charge-4e order parameter, in sharp contrast with a regular (charge-2e) superconductor. Upon lowering temperature, we show that the correlation between charge-4e order and regular interaction terms can drive a first-order phase transition to a charge-2e superconducting state.