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Primordial black holes (PBHs) are dark matter candidates that span broad massranges from $10^{-17}$ $M_\odot$ to $\sim 100$ $M_\odot$. We show that thestochastic gravitational wave background can be a powerful window for thedetection of sub-solar mass PBHs and shed light on their formation channel viathird-generation gravitational wave detectors such as Cosmic Explorer and theEinstein Telescope. By using the mass distribution of the compact objects andthe redshift evolution of the merger rates, we can distinguish astrophysicalsources from PBHs and will be able to constrain the fraction of sub-solar massPBHs $\leq 1$ $M_\odot$ in the form of dark matter $f_{PBH}\leq 1\%$ at $68\%$C.L. even for a pessimistic value of a binary suppression factor. In theabsence of any suppression of the merger rate, constraints on $f_{PBH}$ will beless than $0.001\%$. Furthermore, we will be able to measure the redshiftevolution of the PBH merger rate with about $1\%$ accuracy, making it possibleto uniquely distinguish between the Poisson and clustered PBH scenarios.

Prospects of discovering sub-solar primordial black holes using the stochastic gravitational wave background from third-generation detectors