The effect of disorder on phases across two-dimensional thermal melting

We study melting in a two-dimensional system of classical particles with Gaussian-core interactions in disordered environments. The pure system validates the conventional two-step melting with a hexatic phase intervening between the solid and the liquid. This picture is modified in the presence of pinning impurities. A random distribution of pinning centers forces a hexatic-like low temperature phase that transits into a liquid at a single melting temperature $T^{\rm RP}_{\rm m}$. In contrast, pinning centers located at randomly chosen sites of a perfect crystal anchors a solid at low temperatures which undergoes a direct transition to the liquid at $T^{\rm CP}_{\rm m}$. Thus, the two-step melting is lost in either cases of disorder. We discuss the characteristics of melting depending on the nature of the impurities.