Symmetry breaking in two dimensions on ultrafast timescales

Abstract

The melting of two-dimensional monocrystals is described within the celebrated Kosterlitz‐Thouless‐Halperin‐Nelson‐Young scenario by the dissociation of topological defects. It describes the screening of elasticity due to thermally activated topological defects until shear elasticity disappears. As a well-defined continuous phase transition, freezing and melting should be reversible and independent of history. However, this is not the case: Cooling an isotropic two-dimensional fluid at a finite but nonzero rate does not result in monocrystals. The symmetry cannot be broken globally but only locally within Einstein's event horizon: The slowing down of critical fluctuations forces the system to fall out of equilibrium, resulting in finite-sized domains with a uniform order parameter. For linear cooling rates, the domain size is described by the Kibble‐Zurek mechanism, originally developed for defect formation in the primordial Higgs field shortly after the Big Bang. The size of the domains is a function of the so-called fallout time, the time when the ensemble becomes nonergodic. In the present manuscript, we go beyond the Kibble‐Zurek picture and investigate the limit of the deepest quench on a colloidal monolayer. We resolve the time dependence of structure formation for (local) symmetry breaking when the fallout time is effectively set to zero. However, when quenching instantaneously to various temperatures below the melting point—either deep in the crystalline phase or close to the transition—we find universal behavior if the timescale is rescaled properly.