Abstract
We find that crystalline states of repulsive active Brownian particles at high activity melt into a hexatic state but this transition is not driven by an unbinding of bound dislocation pairs as suggested by the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. Upon reducing the density, the crystalline state melts into a high-density hexatic state devoid of any defects. Decreasing the density further, the dislocations proliferate and introduce plasticity in the system, nevertheless maintaining the hexatic state, but eventually melting into a fluid state. Remarkably, the elastic constants of active solids are equal to those of their passive counterparts, as the swim contribution to the stress tensor is negligible in the solid state. The sole effect of activity is that the stable solid regime shifts to higher densities. Furthermore, discontinuities in the elastic constants as a function of density correspond to changes in the defect concentrations rather than to the solid-hexatic transition.
Highlights
According to the Kosterlitz-Thouless-Halperin-NelsonYoung (KTHNY) theory, a two-dimensional solid of passive particles melts via a continuous transition into an intermediate hexatic state of quasi-long-range bond orientational order and melts subsequently via a second continuous transition into a fluid state [1,2,3]
We hereby assume that the solid state transforms into a hexatic phase when the positional correlations decay with a power-law exponent ηT 1/3 as described by the equilibrium KTHNY theory
We find that the two-step melting scenario consisting of a solid-hexatic transition driven by the unbinding of dislocation pairs and a hexatic-fluid transition caused by defect clusters as observed for the two-dimensional (2D) passive systems of short-range repulsive particles persists at low activity
Summary
According to the Kosterlitz-Thouless-Halperin-NelsonYoung (KTHNY) theory, a two-dimensional solid of passive particles melts via a continuous transition into an intermediate hexatic state of quasi-long-range bond orientational order and melts subsequently via a second continuous transition into a fluid state [1,2,3]. These transitions are triggered by the unbinding of topological defects, which are particles with a nonconforming number of neighbors with respect to that of the crystal lattice. We hereby assume that the solid state transforms into a hexatic phase when the positional correlations decay with a power-law exponent ηT 1/3 as described by the equilibrium KTHNY theory
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