Enigma of Two‐Dimensional Melting in Disordered Environment

ABSTRACT We study melting in two‐dimensional classical particles with Gaussian‐core interactions in both pure and disordered environments. The pure system exhibits conventional two‐step melting described by Berezinskii‐Kosterlitz–Thouless–Halperin–Nelson–Young (BKTHNY) theory, with a hexatic phase separating solid and liquid. Disorder alters this scenario remarkably: random pinning stabilizes a hexatic‐like phase down to zero temperature, which melts directly into a liquid at , whereas commensurate pinning anchors a solid which undergoes a single‐step transition to the liquid at , removing any intervening hexaticity. Thus, in both cases, the two‐step melting of pure systems turns into a one‐step transition. Beyond elucidating the equilibrium phase behavior, with and without disorder, we uncover dynamical signatures of cooperative string‐like motion of particles at very low temperatures. Remarkably, such correlated dynamics, usually associated with structural glasses and supercooled liquids, emerge here within equilibrium phases, in both pure and disordered systems. We further show that impurities, in the form of pinning, enhance such cooperative motions, leading to slow relaxation and departures from diffusive dynamics. Our results highlight the roles of topological defects, impurities, and cooperative dynamics in governing two‐dimensional melting.