  The streaming instability is often invoked as solution to the fragmentation
and drift barriers in planetesimal formation, catalyzing the aggregation of
dust on kyr timescales to grow km-sized cores. However there remains a lack of
consensus on the physical mechanism(s) responsible for initiating it. One
potential avenue is disc photoevaporation, wherein the preferential removal of
relatively dust-free gas increases the disc metallicity. Late in the disc
lifetime, photoevaporation dominates viscous accretion, creating a gradient in
the depleted gas surface density near the location of the gap. This induces a
local pressure maximum that collects drifting dust particles, which may then
become susceptible to the streaming instability. Using a one-dimensional
viscous evolution model of a disc subject to internal X-ray photoevaporation,
we explore the efficacy of this process to build planetestimals. Over a range
of parameters we find that the amount of dust mass converted into planetesimals
is often < 1 M_Earth and at most a few M_Earth spread across tens of AU. We
conclude that photoevaporation may at best be relevant for the formation of
debris discs, rather than a common mechanism for the formation of planetary
cores. Our results are in contrast to a recent, similar investigation that
considered an FUV-driven photoevaporation model and reported the formation of
tens of M_Earth at large (> 100 AU) disc radii. The discrepancies are primarily
a consequence of the different photoevaporation profiles assumed. Until
observations more tightly constrain photoevaporation models, the relevance of
this process to the formation of planets remains uncertain.
