Persistent homology: A tool to understand medium-range order glass structure

Glass structure remains puzzling to scientists, especially due the challenges in characterizing their structural order beyond first coordination shell, i.e., so-called medium-range order. Structural method development is therefore needed advance our understanding of, e.g., structure-property relations these disordered materials. To this end, we here review fundamentals, applications and perspectives of an interesting new approach, namely persistent homology, which a type topological data analysis. This allows for analysis both ring- void-type structures materials without making any assumptions network structure. As discussed herein, it has recently been used analyze atomic position (as obtained from atomistic simulations or reverse Monte Carlo) glasses, regarding We also discuss opportunities coupling homology analyses with machine learning calculations as well open questions that require further investigations.