  We present new constraints on the merging rates of planetary-mass and
asteroid-mass primordial black hole binaries using limits on continuous
waves(quasi-monochromatic, quasi-infinite duration signals) derived from an
all-sky search for isolated compact objects in the first six months of the
third observing run (O3a) of LIGO/Virgo. We calculate the merging rates of
these binaries in a model-independent way, and convert them to constraints on
the primordial black hole abundance with minimal modelling assumptions. Our
results show that we are sensitive to sources at most $\mathcal{O}(10$ pc) away
for systems with chirp masses of $\mathcal{O}(10^{-5}M_\odot)$ at
gravitational-wave frequencies around 30-40 Hz. These results also show that
continuous-wave searches could in the future directly probe the existence of
planetary-mass and asteroid-mass primordial black holes, especially those in
binaries with asymmetric mass ratios. Furthermore, they demonstrate that new
methods accounting for the full nonlinear gravitational-wave frequency
evolution are needed to improve constraints on primordial black holes.
