Persistent homology and many-body atomic structure for medium-range order in the glass

The characterization of the medium-range (MRO) order in amorphous materials and its relation to the short-range order is discussed. A new topological approach to extract a hierarchical structure of amorphous materials is presented, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. This method is called the persistence diagram (PD) and introduces scales to many-body atomic structures to facilitate size and shape characterization. We first illustrate the representation of perfect crystalline and random structures in PDs. Then, the MRO in amorphous silica is characterized using the appropriate PD. The PD approach compresses the size of the data set significantly, to much smaller geometrical summaries, and has considerable potential for application to a wide range of materials, including complex molecular liquids, granular materials, and metallic glasses.