Meng Qingyou, Grason Gregory M
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Phys Rev E. 2021 Sep;104(3-1):034614. doi: 10.1103/PhysRevE.104.034614.
We study the relationship between topological defect formation and ground-state 2D packings in a model of repulsions in external confining potentials. Specifically we consider screened 2D Coulombic repulsions, which conveniently parameterizes the effects of interaction range, but also serves as simple physical model of confined, parallel arrays of polyelectrolyte filaments or vortices in type II superconductors. The countervailing tendencies of repulsions and confinement to, respectively, spread and concentrate particle density leads to an energetic preference for nonuniform densities in the clusters. Ground states in such systems have previously been modeled as conformal crystals, which are composed of locally equitriangular packings whose local areal densities exhibit long-range gradients. Here we assess two theoretical models that connect the preference for nonuniform density to the formation of disclination defects, one of which assumes a continuum distributions of defects, while the second considers the quantized and localized nature of disclinations in hexagonal conformal crystals. Comparing both theoretical descriptions to numerical simulations of discrete particles clusters, we study the influence of interaction range and confining potential on the topological charge, number, and distribution of defects in ground states. We show that treating disclinations as continuously distributable well captures the number of topological defects in the ground state in the regime of long-range interactions, while as interactions become shorter range, it dramatically overpredicts the growth in total defect charge. Detailed analysis of the discretized defect theory suggests that that failure of the continuous defect theory in this limit can be attributed to the asymmetry in the preferred placement of positive vs negative disclinations in the conformal crystal ground states, as well as a strongly asymmetric dependence of self-energy of disclinations on sign of topological charge.
我们在外部约束势中的排斥模型中研究拓扑缺陷形成与基态二维堆积之间的关系。具体而言，我们考虑屏蔽的二维库仑排斥，它方便地参数化了相互作用范围的影响，但也可作为II型超导体中受限的聚电解质细丝或涡旋的平行阵列的简单物理模型。排斥和约束分别使粒子密度扩散和集中的相反趋势导致团簇中能量上倾向于非均匀密度。此类系统中的基态此前被建模为共形晶体，它由局部等三角形堆积组成，其局部面密度呈现长程梯度。在此我们评估两种理论模型，它们将对非均匀密度的偏好与位错缺陷的形成联系起来，其中一种假设缺陷的连续分布，而另一种考虑六边形共形晶体中位错的量子化和局部性质。将这两种理论描述与离散粒子团簇的数值模拟进行比较，我们研究相互作用范围和约束势对基态中缺陷的拓扑电荷、数量和分布的影响。我们表明，将位错视为可连续分布能很好地捕捉长程相互作用 regime 中基态拓扑缺陷的数量，而随着相互作用范围变短，它会大幅高估总缺陷电荷的增长。对离散化缺陷理论的详细分析表明，连续缺陷理论在此极限下的失效可归因于共形晶体基态中正、负位错优先放置的不对称性，以及位错自能对拓扑电荷符号的强烈不对称依赖性。
