arXiv subjects

Patrick Dillmann

Publications and source records attributed to Patrick Dillmann.

4 recordsLinked to original sources

arXiv2024

Symmetry breaking in two dimensions on ultra-fast time scales

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.

cond-mat.soft↗

arXiv2015

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 results in separated domains with different (degenerated) locally broken symmetry. Within this picture we investigate the non-equilibrium dynamics in a condensed matter analogue, a two-dimensional 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.

cond-mat.soft↗

arXiv2014

Spontaneous symmetry breaking in 2D: Kibble-Zurek mechanism in temperature quenched colloidal monolayers

The Kibble-Zurek mechanism describes the formation of topological defects during spontaneous symmetry breaking for quite different systems. Shortly after the big bang, the isotropy of the Higgs-field is broken during the expansion and cooling of the universe. Kibble proposed the formation of monopoles, strings, and membranes in the Higgs field since the phase of the symmetry broken field can not switch globally to gain the same value everywhere in space. Zurek pointed out that the same mechanism is relevant for second order phase transitions in condensed matter systems. Every finite cooling rate induces the system to fall out of equilibrium which is due to the critical slowing down of order parameter fluctuations: the correlation time diverges and the symmetry of the system can not change globally but incorporates defects between different domains. Depending on the cooling rate the heterogeneous order parameter pattern are a fingerprint of critical fluctuations. In the present manuscript we show that a monolayer of superparamagnetic colloidal particles is ideally suited to investigate such phenomena. In thermal equilibrium the system undergos continuous phase transitions according KTHNY-theory. If cooled rapidly across the melting temperature the final state is a polycrystal. We show, that the observations can not be explained with nucleation of a supercooled fluid but is compatible with the Kibble-Zurek mechanism.

cond-mat.soft↗

arXiv2012

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 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 transition for the same experimental data of the given setup. Those criteria are the bond orientational correlation function, the Larson-Grier criterion, 2D dynamic Lindemann parameter, the bond-orientational susceptibility, the 2D Hansen-Verlet rule, the L\"{o}wen-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 works best to identify the hexatic - isotropic liquid transition and the 2D dynamic Lindemann parameter identifies unambiguously the hexatic - crystalline transition.

cond-mat.soft↗