  We study a modification of the primordial black hole (PBH) formation model
from axion bubbles. We assume that the Peccei-Quinn scalar rolls down in the
radial direction from a large field value to the potential minimum during
inflation, which suppresses the axion fluctuations and weakens the clustering
of PBHs on large scales. We find that the modified model can produce a
sufficient number of PBHs that seed the supermassive black holes while avoiding
the observational constraints from isocurvature perturbations and angular
correlation of the high-redshift quasars.
