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Kibble–Zurek mechanism in colloidal monolayers

Significance Spontaneous symmetry breaking describes a variety of transformations from high- to low-temperature phases and applies to cosmological concepts as well as atomic systems. T. W. B. Kibble suggested defect structures (domain walls, strings, and monopoles) to appear during the expansion and cooling of the early universe. The lack of such defects within the visible horizon of the universe mainly motivated inflationary Big Bang theories. W. H. Zurek pointed out that the same principles are relevant within the laboratory when a system obeying a second-order phase transition is cooled at finite rates into the low symmetry phase. Using a colloidal system, we visualize the Kibble–Zurek mechanism on single particle level and clarify its nature in the background of an established microscopic melting formalism. The Kibble–Zurek mechanism describes the evolution of topological defect structures like domain walls, strings, and monopoles when a system is driven through a second-order phase transition. The model is used on very different scales like the Higgs field in the early universe or quantum fluids in condensed matter systems. A defect structure naturally arises during cooling if separated regions are too far apart to communicate (e.g., about their orientation or phase) due to finite signal velocity. This lack of causality results in separated domains with different (degenerated) locally broken symmetry. Within this picture, we investigate the nonequilibrium dynamics in a condensed matter analog, a 2D ensemble of colloidal particles. In equilibrium, it obeys the so-called Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) melting scenario with continuous (second order-like) phase transitions. The ensemble is exposed to a set of finite cooling rates covering roughly three orders of magnitude. Along this process, we analyze the defect and domain structure quantitatively via video microscopy and determine the scaling of the corresponding length scales as a function of the cooling rate. We indeed observe the scaling predicted by the Kibble–Zurek mechanism for the KTHNY universality class.