  Transition metal dichalcogenides have been the subject of numerous studies
addressing technological applications and fundamental issues. Single-layer
PtSe2 is a semiconductor with a trivial bandgap, in contrast, its counterpart
with 25% of Se atoms substituted by Hg, Pt2HgSe3 (jacutingaite, a naturally
occurring mineral), is a 2D topological insulator with a large bandgap. Based
on ab-initio calculations, we investigate the energetic stability, and the
topological transition in Pt(HgxSe1-x)2 as a function of alloy concentration,
and the distribution of Hg atoms embedded in the PtSe2 host. Our findings
reveal the dependence of the topological phase with respect to the alloy
concentration and robustness with respect distribution of Hg. Through a
combination of our ab-initio results and a defect wave function percolation
model, we estimate the random alloy concentration threshold for the topological
transition to be only 9%. Our results expand the possible search for
non-trivial topological phases in random alloy systems.
