Thermal Melting of Two-Dimensional Coulomb Clusters

Ash, Biswarup (2018) Thermal Melting of Two-Dimensional Coulomb Clusters. PhD thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

Phenomena of melting in two-dimensional systems represent one of the most interesting phase transitions in nature. While the concept of phase transition is applicable to bulk systems only, but recent experimental and theoretical studies show that the notion of solid and liquid phases can be attributed to finite systems with small number of particles to characterize the qualitatively different behaviors that resemble the corresponding properties in macroscopic systems. In this thesis, we study the static and dynamic responses of Coulomb interacting particles in two-dimensional confinements across the thermal crossover from solid- to liquid-like behaviors, using Monte Carlo and molecular dynamics simulations. We consider two types of trapping potentials, one is symmetric parabolic (circular) confinement and another is irregular confinement which breaks all spatial symmetries. Through this study, we elucidate the effect of confinement geometry on the physical properties of the system. Analysis of static properties shows that while the positional order is depleted even at zero temperature, still a solid-like a phase can be identified through the strong bond orientational order in the system. Thus, static correlations exhibit the footprints of a hexatic-like phase at low temperature. Surprisingly, dynamics of the particles slow down considerably in this phase – reminiscent of a supercooled liquid. Using density correlations, we probe long-lived heterogeneities arising from the interplay of the irregularity in the confinement and long-range Coulomb interactions. The relaxation at multiple time scales shows a stretched-exponential decay of spatial correlations in irregular traps. We propose a phenomenological model that captures much of the subtleties of our numerical simulations. Temperature dependence of the characteristic time scales, depicting the structural relaxation of the system, show striking similarities with those observed for the glassy systems, indicating that some of the key signatures of supercooled liquids emerge in confinements with lower spatial symmetries. Finally, we analyze the dynamics of particles in irregular Coulomb clusters in terms of normal modes. Using participation ratio and standard tools of random matrix theory, we classify the full normal mode spectrum in localized, quasi-localized and delocalized modes. Further, we demonstrate that at any given temperature, there exists a good correlation between the low-frequency quasi-localized modes and the mobile particles over the structural relaxation time. Establishing this correlation helps in identifying the aspect of a configuration that dictates the heterogeneous dynamics of the particles in the subsequent motion.

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