  We investigate the first-order phase transition catalyzed by primordial black
holes~(PBHs) in the early Universe. We find that super-horizon curvature
perturbations generated in this scenario lead to the production of
gravitational waves when the scalar modes re-enter the horizon. If PBHs with
masses about $10^{-13}M_{\odot}$ constitute all dark matter, the first-order
electroweak phase transition catalyzed by PBHs can explain the gravitational
wave signal observed by pulsar timing array collaborations without the
overproduction of PBHs.
