We introduce the concept of nearly hyperuniform network (NHN) structures as alternatives to the conventional continuous random network (CRN) models for amorphous tetrahedrally coordinated solids, such as amorphous silicon (a-Si). A hyperuniform solid has a structure factor $S\left(k\right)$ that approaches zero as the wavenumber $k\to 0$. We define a NHN as an amorphous network whose structure factor $S(k\to 0)$ is smaller than the liquid value at the melting temperature. Using a novel implementation of the Stillinger-Weber potential for the interatomic interactions, we show that the energy landscape for a spectrum of NHNs includes a sequence of local minima with an increasing degree of hyperuniformity [smaller $S(k\to 0)$] that is significantly below the frozen-liquid value and that correlates with other measurable features in $S\left(k\right)$ at intermediate and large $k$ and with the width of the electronic band gap.

• Received 3 March 2013

DOI:https://doi.org/10.1103/PhysRevB.87.245204