Inversion symmetry breaking induced triply degenerate points in orderly arranged PtSeTe family materials

k paths exactly with [Formula: see text] symmetry allow to find triply degenerate points (TDPs) in band structures. The paths that host the type-II Dirac points in PtSe₂ family materials also have the [Formula: see text] spatial symmetry. However, due to Kramers degeneracy (the systems have both inversion symmetry and time reversal symmetry), the crossing points in them are Dirac ones. In this work, based on symmetry analysis, first-principles calculations, and [Formula: see text] method, we predict that PtSe₂ family materials should undergo topological transitions if the inversion symmetry is broken, i.e. the Dirac fermions in PtSe₂ family materials split into TDPs in PtSeTe family materials (PtSSe, PtSeTe, and PdSeTe) with orderly arranged S/Se (Se/Te). It is different from the case in high-energy physics that breaking inversion symmetry I leads to the splitting of Dirac fermion into Weyl fermions. We also address a possible method to achieve the orderly arranged in PtSeTe family materials in experiments. Our study provides a real example that Dirac points transform into TDPs, and is helpful to investigate the topological transition between Dirac fermions and TDP fermions.