Hidden Hypernetwork and Homology in Vitrification of Ionic Oxides

Disorder in complex systems suppresses long-range order, yet correlated motifs can persist at medium-range order (MRO). In dense ionic networks, these patterns often evade conventional diffraction techniques. Here, we elucidate the hidden hypernetwork consisting of MRO and its role in the vitrification of In–Ga–Zn–O─a prototypical ionic oxide─using persistent homology. In the crystal, hypernetworks form two homological classes─ D 2 (disk) and S 1 (loop)─depending on edge-sharing motifs. D 2 connectivity recovers after vitrification and governs electronic properties. The diversity of MRO in the amorphous phase converges to ∼10 3 atoms, effectively representing the thermodynamic limit. The topological sensitivity based on the stability theorem indicates that Ga plays a key role in MRO reorganization during densification, accompanied by an increasing mobility gap. Our results demonstrate that glassy ionic oxide behavior is driven not by simple disorder but by a reorganized hypernetwork.