Disorder-induced fractionalization of pair density waves

We investigate the effects of disorder on a system that in the clean limit is a pair density wave (PDW) superconductor. The charge order of the clean PDW is inevitably lost (via Imry-Ma), but the fate of the superconducting order is less clear. Here, we consider a strongly inhomogeneous limit in which the system consists of a random collection of PDW puddles embedded in a metallic background. When the puddles are dilute, they become phase coherent at low temperatures, resulting in a state that is macroscopically equivalent to a charge-$2e$ $s$-wave superconductor. This can be viewed as an example of order parameter fractionalization'' -- the PDW order splits into a charge-2e s-wave superconductor and a charge density wave, the latter of which is destroyed by disorder -- and stands in contrast to the vestigial’’ charge-4e superconductivity which has been proposed to arise in weakly disordered PDWs.