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 density fluctuations and are endowed with unique novel physical properties. Here we report the first discovery of disordered hyperuniformity in atomic-scale 2D materials, i.e., amorphous silica composed of a single layer of atoms, based on spectral-density analysis of high-resolution transmission electron microscope images. Subsequent simulations suggest that the observed DHU is closely related to the strong topological and geometrical constraints induced by the local chemical order in the system. Moreover, we show via large-scale density functional theory calculations that DHU leads to almost complete closure of the electronic band gap 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.Disorder hyperuniform (DHU) systems are a unique class of disordered systems which suppress large-scale density fluctuations like crystals and yet possess no Bragg peaks [1, 2]. For a point configuration (e.g., a collection of particle centers of a many-body system), hyperuniformity is manifested as the vanishing structure factor in the infinite-wavelength (or zero-wavenumber) limit, i.e., lim k→0 S(k) = 0, where k = 2π/λ is the wavenumber. In this case of a random field, the hyperuniform condition is given by lim k→0ψ (k) = 0, whereψ(k) is the spectral density [2]. It has been suggested that hyperuniformity can be considered as a new state of matter [1], which possesses a hidden order in between of that of a perfect crystal and a totally disordered system (e.g. a Poisson distribution of points).Recently, a wide spectrum of physical and biological systems have been identified to possess the remarkable property of hyperuniformity, which include the density fluctuations in early universe [3], disordered jammed packing of hard particles [4][5][6][7], certain exotic classical ground states of many-particle systems [8][9][10][11][12][13][14][15], jammed colloidal systems [16][17][18][19], driven non-equilibrium systems [20][21][22][23], certain quantum ground states [24,25], avian photoreceptor patterns [26], organization of adapted im- * These authors contributed equally to this work. † correspondence sent to: xwxfat@gmail.com ‡ correspondence sent to: mohanchen@pku.edu.cn § correspondence sent to: yang.jiao.2@asu.edu ¶ correspondence sent to: hzhuang7@asu.edu mune systems [27], amorphous silicon [28, 29], a wide class of disordered cellular materials [30], dynamic random organizating systems [31-35], and even the distribution of primes on the number axis [36]. In addition, it has been shown that hyperuniform materials can be designed to possess superior physical properties including ...

Single-layer PtN2 exhibits an intriguing structure consisting of a tessellation pattern called the Cairo tessellation of type 2 pentagons, which belong to one of the existing 15 types of convex pentagons discovered so far that can monohedrally tile a plane. Single-layer PtN2 has also been predicted to show semiconducting behavior with direct band gaps. Full exploration of the structureproperty relationship awaits the successful exfoliation or synthesis of this novel single-layer material, which depends on the structure of its bulk counterpart with the same stoichiometry to some extent. Bulk PtN2 with the pyrite structure is commonly regarded as the most stable structure in the literature. But comparing the energies of single-layer PtN2 and bulk PtN2 leads to a dilemma that a single-layer material is more stable than its bulk counterpart. To solve this dilemma, we propose stacking single-layer PtN2 sheets infinitely to form a new bulk structure of PtN2. The resulting tetrahedral layered structure is energetically more stable than the pyrite structure and single-layer PtN2. We also find that the predicted bulk structure is metallic, in contrast to the semiconducting pyrite structure. In addition to predicting the 3D structure, we explore the possibility of rolling single-layer PtN2 sheets into nanotubes. The required energies are comparable to those needed to form carbon or boron nitride nanotubes from their single-layer sheets, implying the feasibility of obtaining PtN2 nanotubes. We finally study the electronic structures of PtN2 nanotubes and find that the band gaps of PtN2 nanotubes are tunable by changing the number of unit cells N of single-layer PtN2 used to construct the nanotubes. Our work shows that dimension engineering of PtN2 not only leads to a more stable 3D structure but also 1D materials with novel properties.

High-entropy alloys (HEAs), which have been intensely studied due to their excellent mechanical properties, generally refer to alloys with multiple equimolar or nearly equimolar elements.According to this definition, Si-Ge-Sn alloys with equal or comparable concentrations of the three Group IV elements belong to the category of HEAs. As a result, the equimolar elements of Si-Ge-Sn alloys likely cause their atomic structures to exhibit the same core effects of metallic HEAs such as lattice distortion. Here we apply density functional theory (DFT) calculations to show that the SiGeSn HEA indeed exhibits a large local distortion effect. Unlike metallic HEAs, our Monte Carlo and DFT calculations show that the SiGeSn HEA exhibits no chemical short-range order due to the similar electronegativity of the constituent elements, thereby increasing the configurational entropy of the SiGeSn HEA. Hybrid density functional calculations show that the SiGeSn HEA remains semiconducting with a band gap of 0.38 eV, promising for economical and compatible mid-infrared optoelectronics applications. We then study the energetics of neutral single Si, Ge, and Sn vacancies and (expectedly) find wide distributions of vacancy formation energies, similar to those found in metallic HEAs. However, we also find anomalously small lower bounds (e.g., 0.04 eV for a Si vacancy) in the energy distributions, which arise from the bond reformation near the vacancy. Such small vacancy formation energies and their associated bond reformations retain the semiconducting behavior of the SiGeSn HEA, which may be a signature feature of a semiconducting HEA that differentiates from metallic HEAs.

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