Ormrod Morley David, Salmon Philip S, Wilson Mark
Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom.
Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom.
J Chem Phys. 2021 Mar 28;154(12):124109. doi: 10.1063/5.0040393.
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 B (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.
通过持久同调分析研究二维网络材料的拓扑结构。二维的限制使得关键的持久同调度量（持久图、圈和贝蒂数）能够与更传统的度量（如环尺寸分布）进行直接比较。采用了两种不同类型的网络，其中拓扑结构被系统地操控。第一种是为三角形筏模型生成相对刚性的网络，其代表了如二氧化硅双层等材料。第二种是使用键切换算法生成更灵活的网络，其代表了如石墨烯等材料。通过参考与扭曲多边形相关的长度尺度在持久图中识别能带。具有最大有序性的三角形筏模型允许将特定的能带B（n = 1, 2, 3, …）分配给由n个键分隔的原子构型。更无序网络模型的持久图也显示出能带，尽管不太明显。持久同调方法由此提供了从结构因子或径向分布函数无法获得的关于n体相关性的信息。对持久圈的分析给出了原始环统计，前提是无序程度不太大。该方法还给出了从环统计分析中无法获得的关于环的规则性的信息。持久同调方法在应用于实验获得的二氧化硅双层和石墨烯构型时展示了其效用。
