Persistent homology in two-dimensional atomic networks.
Persistent homology in two-dimensional atomic networks.
复制标题
二维原子网络中的持久同源性。
DOI：
10.1063/5.0040393
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
M. Wilson
中科院分区：
文献类型：
--
作者：
David Ormrod Morley;P. Salmon;M. Wilson
用持久同调分析方法研究了二维网络材料的拓扑结构。两个维度的约束允许将关键的持久同源指标(持久性图、周期和Betti数)与更传统的指标(如环大小分布)进行直接比较。采用了两种不同类型的网络，其中系统地操纵了拓扑。首先，对于代表二氧化硅双层膜等材料的三角形筏板模型，生成了相对刚性的网络。在第二种方法中，使用键转换算法生成了更灵活的网络，这是石墨烯等材料的代表。在持久性图中，通过参考与扭曲的多边形相关联的长度标尺来标识频带。具有最大排序的三角形-RAFT模型允许特定的带Bn(n=1，2，3，…)被分配到由n个键分隔的原子的构型。更无序的网络模型的持久性图也显示出条带，尽管不那么明显。持久同源方法由此提供了关于不能从结构因子或径向分布函数获得的n体关联的信息。在无序程度不太大的情况下，对持续循环的分析给出了本原环的统计数据。该方法还给出了环的正则性的信息，这是环统计分析所不能获得的。通过对实验获得的二氧化硅双层膜和石墨烯构型的应用，证明了持久同源方法的实用性。
The topology of two-dimensional network materials is investigated by persistent homology analysis. The constraint of two dimensions allows for a direct comparison of key persistent homology metrics (persistence diagrams, cycles, and Betti numbers) with more traditional metrics such as the ring-size distributions. Two different types of networks are employed in which the topology is manipulated systematically. In the first, comparatively rigid networks are generated for a triangle-raft model, which are representative of materials such as silica bilayers. In the second, more flexible networks are generated using a bond-switching algorithm, which are representative of materials such as graphene. Bands are identified in the persistence diagrams by reference to the length scales associated with distorted polygons. The triangle-raft models with the largest ordering allow specific bands Bn (n = 1, 2, 3, …) to be allocated to configurations of atoms separated by n bonds. The persistence diagrams for the more disordered network models also display bands albeit less pronounced. The persistent homology method thereby provides information on n-body correlations that is not accessible from structure factors or radial distribution functions. An analysis of the persistent cycles gives the primitive ring statistics, provided the level of disorder is not too large. The method also gives information on the regularity of rings that is unavailable from a ring-statistics analysis. The utility of the persistent homology method is demonstrated by its application to experimentally-obtained configurations of silica bilayers and graphene.