Density Of Topological Defects Research Articles

Topological transition to rest in the electrohydrodynamics of nematics

ABSTRACT Some nematic liquid crystals undergo electro-convective instabilities if forced by a low-frequency oscillating electric field. When the forcing amplitude is increased, a series of bifurcations occurs, which correspond to increasing disorder and reduction of the size of the electro-convective rolls. At a threshold, a transition to an electrohydrodynamic state characterised by a high density of topological defects occurs. Here, we show that in some nematic mixtures this transition is replaced by a topological transition to rest, that is, the electrohydrodynamics are quenched by the nucleation of a state that is topologically non-equivalent to the initial texture of the nematic.

Two-Dimensional Melting of Two- and Three-Component Mixtures.

We elucidate the interplay between diverse two-dimensional melting pathways and establish solid-hexatic and hexatic-liquid transition criteria via the numerical simulations of the melting transition of two- and three-component mixtures of hard polygons and disks. We show that a mixture's melting pathway may differ from its components and demonstrate eutectic mixtures that crystallize at a higher density than their pure components. Comparing the melting scenario of many two- and three-component mixtures, we establish universal melting criteria: the solid and hexatic phases become unstable as the density of topological defects, respectively, overcomes ρ_{d,s}≃0.046 and ρ_{d,h}≃0.123.

Adiabatic-impulse approximation in the non-Hermitian Landau-Zener model

In the non-Hermitian Landau-Zener models, we investigate the dynamical transition both in parity-time symmetric and symmetry-broken regimes. Taking into account the complex nature of the energy of the non-Hermitian systems, the absolute value of the gap was used to determine the relaxation rate of the system. To show the dynamics of the phase transitions, the relative population is used to estimate the topological defect density in nonequilibrium phase transitions, rather than the excitations in the corresponding Hermitian systems. The result shows that the adiabatic-impulse approximation, which is fundamental to the Kibble-Zurek mechanism, may be adapted to the parity-time symmetric non-Hermitian Landau-Zener models to examine the dynamics near the critical point. The most basic non-Hermitian two-level models with an exact solution exhibiting the Kibble-Zurek mechanism are presented. It would be interesting to extend this scenario to quantum many-body models, such as the quantum phase transition in the Ising model.

E-cadherin-dependent coordinated epithelial rotation on a two-dimensional discoidal pattern.

In vivo, cells collectively migrate in a variety of developmental and pathological contexts. Coordinated epithelial rotation represents a unique type of collective cell migrations, which has been modeled in vitro under spatially confined conditions. Although it is known that the coordinated rotation depends on intercellular interactions, the contribution of E-cadherin, a major cell-cell adhesion molecule, has not been directly addressed on two-dimensional (2D) confined substrates. Here, using well-controlled fibronectin-coated surfaces, we tracked and compared the migratory behaviors of MDCK cells expressing or lacking E-cadherin. We observed that wild-type MDCK II cells exhibited persistent and coordinated rotations on discoidal patterns, while E-cadherin knockout cells migrated in a less coordinated manner without large-scale rotation. Our comparison of the collective dynamics between these two cell types revealed a series of changes in migratory behavior caused by the loss of E-cadherin, including a decreased global migration speed, less regularity in quantified coordination, and increased average density of topological defects. Taken together, these data demonstrate that spontaneous initiation of collective epithelial rotations depends on E-cadherin under 2D discoidal confinements.

Quench dynamics and scaling laws in topological nodal loop semimetals

We employ quench dynamics as an effective tool to probe different universality classes of topological phase transitions. Specifically, we study a model encompassing both Dirac-like and nodal loop criticalities. Examining the Kibble-Zurek scaling of topological defect density, we discover that the scaling exponent is reduced in the presence of extended nodal loop gap closures. For a quench through a multicritical point, we also unveil a path-dependent crossover between two sets of critical exponents. Bloch state tomography finally reveals additional differences in the defect trajectories for sudden quenches. While the Dirac transition permits a static trajectory under specific initial conditions, we find that the underlying nodal loop leads to complex time-dependent trajectories in general. In the presence of a nodal loop, we find, generically, a mismatch between the momentum modes where topological defects are generated and where dynamical quantum phase transitions occur. We also find notable exceptions where this correspondence breaks down completely.

Nematic order condensation and topological defects in inertial active nematics.

Living materials at different length scales manifest active nematic features such as orientational order, nematic topological defects, and active nematic turbulence. Using numerical simulations we investigate the impact of fluid inertia on the collective pattern formation in active nematics. We show that an incremental increase in inertial effects due to reduced viscosity results in gradual melting of nematic order with an increase in topological defect density before a discontinuous transition to a vortex-condensate state. The emergent vortex-condensate state at low enough viscosities coincides with nematic order condensation within the giant vortices and the drop in the density of topological defects. We further show flow field around topological defects is substantially affected by inertial effects. Moreover, we demonstrate the strong dependence of the kinetic energy spectrum on the inertial effects, recover the Kolmogorov scaling within the vortex-condensate phase, but find no evidence of universal scaling at higher viscosities. The findings reveal complexities in active nematic turbulence and emphasize the important cross-talk between active and inertial effects in setting flow and orientational organization of active particles.

Approaching the Topological Low-Energy Physics of the F Model in a Two-Dimensional Magnetic Lattice.

We demonstrate that the physics of the F model can be approached very closely in a two-dimensional artificial magnetic system. Faraday lines spanning across the lattice and carrying a net polarization, together with chiral Faraday loops characterized by a zero magnetic susceptibility, are imaged in real space using magnetic force microscopy. Our measurements reveal the proliferation of Faraday lines and Faraday loops as the system is brought from low- to high-energy magnetic configurations. They also reveal a link between the Faraday loop density and icelike spin-spin correlations in the magnetic structure factor. Key for this Letter, the density of topological defects remains small, on the order of 1% or less, and negligible compared to the density of Faraday loops. This is made possible by replacing the spin degree of freedom used in conventional lattices of interacting nanomagnets by a micromagnetic knob, which can be finely tuned to adjust the vertex energy directly, rather than modifying the two-body interactions.

Kibble-Zurek mechanism for nonequilibrium phase transitions in driven systems with quenched disorder

We show that the Kibble-Zurek mechanism applies to nonequilibrium phase transitions found in driven assemblies of superconducting vortices and colloids moving over quenched disorder where a transition occurs from a plastic disordered flowing state to a moving anisotropic crystal. We measure the density of topological defects as a function of quench rate through the nonequilibrium phase transition, and find that on the ordered side of the transition, the topological defect density ρd scales as a power law, {rho }_{{{{{{{{rm{d}}}}}}}}}propto 1/{t}_{{{{{{{{rm{q}}}}}}}}}^{beta }, where tq is the quench time duration, consistent with the Kibble-Zurek mechanism. We show that scaling with the same exponent holds for varied strengths of quenched disorder and that the exponents fall in the directed percolation universality class. Our results suggest that the Kibble-Zurek mechanism can be applied to the broader class of systems that exhibit absorbing phase transitions.

Scaling theory of the Kosterlitz-Thouless phase transition

We propose a series of scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their interplay, are considered. Relaxation times of both a normal power-law and an anomalous power-law with a logarithmic factor are studied. Finite-size and finite-entanglement scaling forms somehow similar to but different from a frequently employed ansatz are presented. The Kibble-Zurek scaling of topological defect density for a linear driving across the KT transition point is investigated in detail. An implicit equation for a rate exponent in the theory is derived, and the exponent varies with the distance from the critical point and the driving rate consistent with relevant experiments. To verify the theories, we utilize the KT phase transition of a one-dimensional Bose-Hubbard model. The infinite time-evolving-block-decimation algorithm is employed to solve numerically the model for finite bond dimensions. Both a correlation length and an entanglement entropy in imaginary time and only the entanglement entropy in real-time driving are computed. Both the short-time critical dynamics in imaginary time and the finite-time scaling in real-time driving, both including the finite bond dimension, for the measured quantities are found to describe the numerical results quite well via surface collapses. The critical point is also estimated and confirmed to be 0.302(1) at the infinite bond dimension on the basis of the scaling theories.

Melting of two-dimensional biological tissues containing active Ornstein–Uhlenbeck cells

The solid–liquid transition of biological tissues is numerically investigated in the presence of Ornstein–Uhlenbeck noise. We demonstrate that the melting scenario of the system is controlled by three parameters: temperature, the persistence time that controls the nonequilibrium properties of the system, and the target shape index that characterizes the competition between cell–cell adhesion and cortical tension. An increase in the persistence time always causes the system to transition from disordered (liquid state) to ordered (solid state). For stiff cells (small target shape index), on increasing temperature, the system undergoes the first order melting for short persistence time, while it undergoes a continuous solid–hexatic transition followed by a discontinuous hexatic–liquid transition for long persistence time. For soft cells (large target shape index), the melting always occurs via a continuous solid–hexatic transition followed by a discontinuous hexatic–liquid transition and the parameter range where the hexatic phase occurs increases with the persistence time. These behaviors are confirmed by the evolution of the density of topological defects. The phase diagrams of the system are also presented based on three parameters (temperature, the shape index, and the persistence time). Our study may contribute to the understanding of melting in two dimensional systems with many-body interactions and deformable particles.

Kibble-Zurek mechanism in polariton graphene

We study the formation of topological defects (quantum vortices) during the formation of a 2D polariton condensate at the $\Gamma$ point of a honeycomb lattice via the Kibble-Zurek mechanism. The lattice modifies the single-particle dispersion. The typical interaction energies at the quench time correspond to the linear part of the dispersion. The resulting scaling exponent for the density of topological defects is numerically found as $0.95\pm0.05$. This value differs from the one expected for 2D massive particles (1/2), but is indeed compatible with the one expected for a linear dispersion. We moreover demonstrate that the vortices can be pinned to the lattice, which prevents their recombination and could facilitate their observation and counting in continuous wave experiments.

Rational Control of Topological Defects in Porous Carbon for High‐Efficiency Carbon Dioxide Conversion

AbstractNitrogen‐doped porous carbons have been extensively studied for electrocatalysis, including the electrocatalytic CO2 reduction reaction. Most relevant studies have focused on nitrogen sites in porous carbons, however, the intrinsic topological defects of porous carbons have been usually ignored because of difficulties in controllable preparation, structural identification, and determining structure–property correlations. In this study, topological defect‐enriched porous carbons are fabricated through pyridinic‐N volatilization at a high temperature by using nitrogen‐enriched 2,6‐dicyanopyridine as the precursor. As‐prepared porous carbons possess rich topological defects and ultrahigh specific surface area of up to 3123 m2 g−1. As electrocatalysts for CO2 reduction, as‐prepared porous carbons exhibit excellent activity for CO formation with a low onset potential of −283 mV, high CO Faradaic efficiency of up to 99.0% at −0.4 V, which is the state‐of‐the‐art activity among all of reported porous carbons. Density functional theory calculations indicate that pentagonal structure cause the electronegativity of carbon skeletons and act as the main active sites for CO2 reduction. This work not only presents a facile approach for fabricating porous carbons with a high density of topological defects for efficient electrocatalytic CO2 reduction but also provides insights regarding the origin of high activity of topological defects in porous carbons.

Quench dynamics in 1D model with 3rd-nearest-neighbor hoppings* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11974334, 11574294, and 11774332).

The non-equilibrium dynamics of a one-dimensional (1D) topological system with 3rd-nearest-neighbor hopping has been investigated by analytical and numerical methods. An analytical form of topological defect density under the periodic boundary conditions (PBC) is obtained by using the Landau–Zener formula (LZF), which is consistent with the scaling of defect production provided by the Kibble–Zurek mechanism (KZM). Under the open boundary conditions (OBC), quench dynamics becomes more complicated due to edge states. The behaviors of the system quenching across different phases show that defect production no longer satisfies the KZM paradigm since complicated couplings exist under OBC. Some new dynamical features are revealed.

Experimental measures of topological sector fluctuations in the F-model

The two dimensional F-model is an ice-rule obeying model, with a low temperature antiferroelectric state and high temperature critical Coulomb phase. Polarization in the system is associated with topological defects in the form of system-spanning windings which makes it an ideal system on which to observe topological sector fluctuations, as have been discussed in the context of spin ice and Berezinskii-Kosterlitz-Thouless (BKT) systems. Here we develop Lieb and Baxter's historic solutions of the F-model to exactly calculate relevant properties, several apparently for the first time. We further calculate properties not amenable to exact solution by an approximate cavity method and by referring to established scaling results. Of particular relevance to topological sector fluctuations are the exact results for the applied field polarization and the "energetic susceptibility". The latter is a both a measure of topological sector fluctuations and, surprisingly, in this case, a measure of the order parameter correlation exponent. In the high temperature phase, the temperature tunes the density of topological defects and algebraic correlations, with the energetic susceptibility undergoing a jump to zero at the antiferroelectric ordering temperature, analogous to the "universal jump" in BKT systems. We discuss how these results are relevant to experimental systems, including to spin ice thin films and three-dimensional dipolar spin ice and water ice, where we find that an analogous "universal jump" has previously been established in numerical studies. This unexpected result suggests a universal limit on the stability of perturbed Coulomb phases that is independent of dimension and of the order of the transition. Experimental results on water ice Ih are not inconsistent with this proposition. We complete the paper by relating our results to experimental studies of artificial spin ice arrays.

Phase behavior of Lennard-Jones particles in two dimensions

The phase diagram of the prototypical two-dimensional Lennard-Jones (LJ) system, while extensively investigated, is still debated. In particular, there are controversial results in the literature with regard to the existence of the hexatic phase and the melting scenario. Here we study the phase behavior of two-dimensional range-limited LJ particles via large-scale numerical simulations. We demonstrate that at a high temperature, when the attraction in the potential plays a minor role, melting occurs via a continuous solid-hexatic transition followed by a first-order hexatic-fluid transition. The hexatic phase occurs in a density range that vanishes as the temperature decreases so that at low-temperature melting occurs via a first-order liquid-solid transition. The temperature where the hexatic phase disappears is well above the liquid-gas critical temperature. The evolution of the density of topological defects confirms this scenario.

Formation and stability of conformal spirals in confined 2D crystals

We investigate the ground-state and dynamical properties of nonuniform two-dimensional (2D) clusters of long-range interacting particles. We demonstrate that, when the confining external potential is designed to produce an approximate 1/r 2 density profile, the particles crystallize into highly ordered structures featuring spiral crystalline lines. Despite the strong inhomogeneity of the observed configurations, most of them are characterized by small density of topological defects, typical of conformal crystals, and the net topological charge induced by the simply-connected geometry of the system is concentrated near the cluster center. These crystals are shown to be robust with respect to thermal fluctuations up to a certain threshold temperature, above which the net charge is progressively redistributed from the center to the rest of the system and the topological order is lost. The crystals are also resilient to the shear stress produced by a small nonuniform azimuthal force field, rotating as a rigid body (RB). For larger forces, topological defects proliferate and the RB rotation gives place to plastic flow.

Ammonia Thermal Treatment Toward Topological Defects in Porous Carbon for Enhanced Carbon Dioxide Electroreduction

The design of specific active sites for the carbon dioxide electro-reduction reaction (CO2RR), is crucial for determining product selectivity and catalysis performance. Here, we present an efficient NH3 thermal treatment for thoroughly removing the pyrrolic-N and pyridinic-N dopants from 3D N-enriched graphene analogue particles, to create high density of topological defects as active sites for CO2RR.[1] Firstly we found that NH3 showed a pronounced effect of eliminating specific N-containing moieties at elevated temperatures, superior to Ar. The identification of topological defects (pentagonal carbon polygon and 585 defect) was investigated by near-edge X-ray absorption fine structure measurements and local density of states analysis, and its formation mechanism was revealed by reactive molecular dynamics simulations.The as-prepared catalysts exhibited excellent performance in flooded half-cell experiments in 0.1 M KHCO3 reaching current densities of 2.8 mA cm-2 and 4.4 mA cm-2 with FECO of 92.7% and 89.2% at -0.6 V and -0.7 V v.s. RHE, respectively at room temperature and atmosphere pressure. These results are among the best performances reported for metal-free catalysts.[2,3,4,5] Density functional theory calculations revealed that the edged pentagonal sites (penta-1 and 585-1 defects) are the dominating active centers with the lowest free energy barriers of CO2RR for CO production.[6,7] References [1] Zhu J.; Huang J.; Mei W. et al, Angew. Chem. Int. Ed. 2019, 58, 3859-3864[2] Wu, J.; Liu, M.; Sharma, P. P. et al, Nano Lett. 2016, 16 (1), 466-70[3] Wu, J.; Yadav, R. M.; Liu, M. et al, ACS Nano 2015, 9 (5), 5364-5371.[4] Daiyan, R.; Tan, X.; Chen, R. et al, Acs Energy Lett. 2018, 3 (9), 2292-2298.[5] Kumar, B.; Asadi, M.; Pisasale, D. et al, Nat. Commun. 2013, 4, 2819.[6] Banhart F., Kotakoski J., Krasheninnikov A.V. ACS Nano, 2011 , 5, 29-41.[7] Dong, Y.,zhang Q.J. et al, Ammonia Thermal Treatment toward Topological Defects in Porous Carbon for Enhanced Carbon Dioxide Electroreduction. (submitted) Figure 1

Cosmic microwave background dipole asymmetry could be explained by axion monodromy cosmic strings

Observations by the Wilkinson Microwave Anisotropy Probe and the Planck mission suggest a hemispherical power amplitude asymmetry in the cosmic microwave background, with a correlation length on the order of the size of the observable Universe. We find that this anomaly can be naturally explained by an axion-like particle (ALP) cosmic string formed near our visible Universe. The field variation associated to this cosmic string creates particle density fluctuations after inflation, which consequently decay into radiation before the Big Bang Nucleosynthesis (BBN) era and resulted in the observed power asymmetry. We find in this scenario that the hemispherical power amplitude asymmetry is strongly scale dependent: $A(k)\propto {\rm exp}(-kl)/k$. Admittedly, typical inflation models predict a relic number density of topological defects of order one per observable Universe and so in our model the cosmic string must be tuned to have an impact factor of order $1/H_0$. Interestingly, the constraints based on purely cosmological considerations also give rise to a Peccei-Quinn scale $F_a$ of order $10^3$ larger then the Hubble scale of inflation $H_I$. Assuming $H_I\sim 10^{13}$GeV, we then have an ALP with $F_a\sim 10^{16}$GeV, which coincides with the presumed scale of grand unification. As we require ALP decays occur before the BBN era, which implies a relatively heavy mass or strong self-coupling, and considering that the associated potential should break the shift symmetry softly in order to protect the system from radiative corrections, we also conclude that the required ALP potential should be monodromic in nature.

Critical density of topological defects upon a continuous phase transition

Using extensive Monte Carlo simulations, we test the hypothesis that the density of corresponding topological defects has a universal value at the temperature of a continuous phase transition. We consider several simple two-dimensional models where domain walls, vortices, so-called Z2 vortices or their combinations are presented. These topological defects are relevant correspondingly to an Ising second-order phase transition, a Berezinskii–Kosterlitz–Thouless transition and an explicit crossover. We compare results for square and triangular lattices as well as for the complicated situation when two types of defects are presented and two transitions occur separated in temperature. All considered cases demonstrate consentient results confirming the hypothesis.

Glass as a Medium with a High Density of Topological Defects

A mechanism for the appearance of shear rigidity is proposed for disordered systems, the structure of which can be described as a medium with a high density of linear topological defects. This mechanism consists in kink localization in dislocation lines, which limits their mobility. This approach can be used to determine the temperature dependence of plastic deformation, to relate it to the fractal dimension of a set of defects, and to explain the dependence of the glass transition temperature on the cooling rate.