Disordered hyperuniformity in two-dimensional amorphous silica.

Disordered hyperuniformity (DHU) is a recently proposed new state of matter, which has been observed in a variety of classical and quantum many-body systems. DHU systems are characterized by vanishing infinite-wavelength normalized density fluctuations and are endowed with unique novel physical properties. Here, we report the discovery of disordered hyperuniformity in atomic-scale two-dimensional materials, i.e., amorphous silica composed of a single layer of atoms, based on spectral-density analysis of high-resolution transmission electron microscopy images. Moreover, we show via large-scale density functional theory calculations that DHU leads to almost complete closure of the electronic bandgap compared to the crystalline counterpart, making the material effectively a metal. This is in contrast to the conventional wisdom that disorder generally diminishes electronic transport and is due to the unique electron wave localization induced by the topological defects in the DHU state.