  We perform a search for binary black hole mergers with one subsolar mass
black hole and a primary component above $2 M_\odot$ in the second observing
run of LIGO/Virgo. Our analysis therefore extends previous searches into a mass
region motivated by the presence of a peak in any broad mass distribution of
primordial black holes (PBHs) around $[2-3] M_\odot$ coming from the equation
of state reduction at the QCD transition. Four candidate events are found
passing a false alarm rate (FAR) threshold of 2 per year, although none are
statistically significant enough for being clear detections. We first derive
model independent limits on the PBH merging rates assuming a null result of the
search. Then we confront them to two recent scenarios in which PBHs can
constitute up to the totality of the Dark Matter, explain LIGO/Virgo mergers
and the possible observation of a stochastic gravitational-wave background by
NANOGrav. We find that these models still pass the rate limits and conclude
that the analysis of the O3 and O4 observing runs will be decisive to test the
hypothesis of a primordial origin of black hole mergers.
