Kibble-Zurek mechanism in colloidal monolayers.

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.

Comparison of 2D melting criteria in a colloidal system.

We use super-paramagnetic spherical particles which are arranged in a two-dimensional monolayer at a water/air interface to investigate the crystal to liquid phase transition. According to the KTHNY theory a crystal melts in thermal equilibrium by two continuous phase transitions into the isotropic liquid state with an intermediate phase, commonly known as the hexatic phase. We verify the significance of several criteria based on dynamical and structural properties to identify the crystal-hexatic and hexatic-isotropic liquid phase transitions for the same experimental data of the given setup. The criteria are the bond orientational correlation function, the Larson-Grier criterion, the 2D dynamic Lindemann parameter, the bond orientational susceptibility, the 2D Hansen-Verlet rule, the Löwen-Palberg-Simon criterion as well as a criterion based on the shape factor of Voronoi cells and Minkowski functionals. For our system with long-range repulsion, the bond order correlation function and bond order susceptibility work best to identify the hexatic-isotropic liquid transition and the 2D dynamic Lindemann parameter identifies unambiguously the hexatic-crystalline transition.