Symmetry breaking in two dimensions on ultra-fast time scales

TL;DR

This paper investigates the rapid symmetry breaking process in two-dimensional colloidal monolayers during deep quenches, revealing universal behavior in structure formation when timescales are properly scaled, challenging traditional views on phase transition reversibility.

Contribution

It introduces a detailed analysis of ultra-fast symmetry breaking in 2D systems during deep quenches, extending the Kibble-Zurek mechanism to new regimes and timescales.

Findings

Universal behavior in structure formation during deep quenches.

Symmetry breaking occurs locally due to critical slowing down.

Deep quenches lead to finite domain sizes consistent with Kibble-Zurek predictions.

Abstract

Melting of two-dimensional mono-crystals is described within the celebrated Kosterlitz-Thouless-Halperin-Nelson-Young scenario (KTHNY-Theory) by the dissociation of topological defects. It describes the shielding 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 2D fluid with a finite but nonzero rate does not end in mono-crystals. The symmetry can not be broken globally but only locally in the thermodynamic limit due to the critical slowing down of order parameter fluctuations. This results in finite sized domains with the same order parameter. For linear cooling rates, the domain size is described by the Kibble-Zurek mechanism, originally developed for the defect formation of the primordial Higgs-field shortly after the Big-Bang. In the present manuscript, we investigate the limit of the deepest descent quench on a colloidal monolayer and resolve the time dependence of structure formation for (local) symmetry breaking. Quenching to various target temperatures below the melting point (deep in the crystalline phase and just close to the transition), we find universal behaviour if the timescale is re-scaled properly.