Disordered hyperuniform networks and their application in atomic-scale low-dimensional materials*

Disordered hyperuniformity is a recently discovered novel state of many-body systems that possesses vanishing normalized infinite-wavelength density fluctuations and a hidden long-range order similar to a perfect crystal, and yet is statistically isotropic with no Bragg peaks like a liquid or glass. In this work we present a series of research centered around a new concept called "disordered hyperuniform quantum materials", i.e., disordered hyperuniform atomic-scale low-dimensional materials where quantum effects are significant. In particular, we discover a hyperuniformity-preserving topological transformation in two-dimensional networks that involves continuous introduction of Stone-Wales (SW) defects. Our findings have important implications for amorphous 2D materials such as graphene and silica. Importantly, we find that when adding disorder in a hyperuniform manner, silica systems exhibit a transition from insulating to metallic behavior, which is in contrast to the conventional wisdom that disorder generally diminishes electronic transport.