Nonequilibrium critical dynamics of a Kosterlitz-Thouless-transition

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Using a colloidal ensemble in two dimensions, we will investigate the formation of topological defects while pushing the system far from thermal equilibrium through a continuous phase transition.In equilibrium melting of two-dimensional (2D) mono-crystals is described by the celebrated Kosterlitz-Thouless-Halperin-Nelson-Young scenario (KTHNY-Theory). In this theory the dissociation of thermally activated topological defects destroys positional and orientational order. For a well-defined continuous phase transitions as predicted by KTHNY-theory, melting and freezing should be reversible and independent of the history of the material. However, this is not the case and time reversal is not fulfilled as we demonstrated recently in previous work. An isotropic two-dimensional fluid never freezes into a mono-crystal but becomes highly poly-crystalline if cooled with a non-zero rate. We observed that symmetry breaking does not happen globally and defects are frozen in. Moreover, we showed that our observation support the Kibble-Zurek-mechanism (KZM) for slow (linear) cooling rates.The Kibble-Zurek mechanism was originally developed by Tom Kibble to describe the defect density of the primordial Higgs-field while cooled by expansion of the early universe shortly after Big Bang. Regions being separated far enough in space, such that they cannot communicate even with the speed of light, cannot gain the same order-parameter during spontaneous symmetry breaking. W. Zurek transferred the idea to condensed matter and quantum fluids. Due to critical slowing down of order parameter fluctuations during cooling (correlation times tend to infinity), the system must fall out of equilibrium and defects like monopoles and grain boundaries are incorporated into the low temperature phase.We will investigate those phenomena with a colloidal monolayer of micrometer sized super-paramagnetic particles, which perform Brownian motion and are confined to an absolutely flat interface. Unlike “real” atoms, particles are large AND slow enough that they can easily be monitored with video-microscopy on single particle level at any relevant time scale. Due to their super-paramagnetism we can quench our ensembles on times scales, orders of magnitudes faster than the shortest intrinsic time scale given by the Brownian time (~ sec). In atomic systems this time is < 10^-10sec and additionally the heat flux is limited. Cooling rates on unrivalled fast time scales are possible for colloids, entering a time region practically inaccessible in condensed matter and strictly inaccessible in the primordial Higgs-field.For ultrafast quenches I propose the domain-size distribution not to depend on the super-cooling after the quench. Instead, in strong contrast to nucleation, it will depend on the order-parameter fluctuations before the quench and the very early stage of local symmetry breaking.