Persistent homology in two-dimensional atomic networks

Area of Science:

• Materials Science
• Computational Topology
• Condensed Matter Physics

Background:

• Understanding the topology of 2D network materials is crucial for predicting their properties.
• Traditional metrics like ring-size distributions offer limited insights into complex network structures.

Purpose of the Study:

• To investigate the topology of 2D network materials using persistent homology analysis.
• To compare persistent homology metrics with traditional metrics for network characterization.

Main Methods:

• Systematic manipulation of network topology in triangle-raft and bond-switching models.
• Application of persistent homology analysis, including persistence diagrams, cycles, and Betti numbers.
• Comparison with ring-size distributions, structure factors, and radial distribution functions.

Main Results:

• Bands in persistence diagrams correlate with atomic configurations separated by n bonds.
• Persistent homology provides information on n-body correlations beyond traditional methods.
• Analysis of persistent cycles yields primitive ring statistics and ring regularity.

Conclusions:

• Persistent homology is a powerful tool for characterizing the topology of 2D network materials.
• The method reveals n-body correlations and ring regularity in materials like silica bilayers and graphene.
• This approach offers novel insights not accessible through conventional structural analysis.