  The possibility that primordial black holes (PBHs) form a part of dark matter
has been considered for a long time but poorly constrained over a wide mass
range. Fast radio bursts (FRBs) are bright radio transients with millisecond
duration. Lensing effect of them has been proposed as one of the cleanest
probes for constraining the presence of PBHs in the stellar mass window. In
this paper, we first apply the normalised cross-correlation algorithm to search
and identify candidates of lensed FRBs in the latest public FRB observations,
i.e. $593$ FRBs which mainly consist of the first Canadian Hydrogen Intensity
Mapping Experiment FRB catalog, and then derive constraints on the abundance of
PBHs from the null search result of lensing signature. For a monochromatic mass
distribution, the fraction of dark matter made up of PBHs could be constrained
to $\leq87\%$ for $\geq500~M_{\odot}$ at 95\% confidence level by assuming flux
ratio thresholds dependent signal-to-noise ratio for each FRB and that
apparently one-off events are intrinsic single bursts. This result would be
improved by a three times factor when a conventional constant flux ratio
threshold is considered. Moreover, we derive constraints on PBHs with a
log-normal mass function naturally predicted by some popular inflation models
and often investigated with gravitational wave detections. We find that, in
this mass distribution scenario, the constraint from currently public FRB
observations is relatively weaker than the one from gravitational wave
detections. It is foreseen that upcoming complementary multi-messenger
observations will yield considerable constraints on the possibilities of PBHs
in this intriguing mass window.
