Dimension engineering of single-layer PtN 2 with the Cairo tessellation

Single-layer PtN 2 exhibits an intriguing structure consisting of a tessellation pattern called the Cairo tessellation of type 2 pentagons, which belongs to one of the existing 15 types of convex pentagons discovered so far that can monohedrally tile a plane. Single-layer PtN 2 has also been predicted to show semiconducting behavior with direct bandgaps. Full exploration of the structure-property 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 PtN 2 with the pyrite structure is commonly regarded as the most stable structure in the literature. But comparing the energies of single-layer PtN 2 and bulk PtN 2 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 PtN 2 sheets infinitely to form a new bulk structure of PtN 2. The resulting tetragonal layered structure is energetically more stable than the pyrite structure and single-layer PtN 2. 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 PtN 2 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 PtN 2 nanotubes. We finally study the electronic structures of PtN 2 nanotubes and find that the bandgaps of PtN 2 nanotubes are tunable by changing the number of unit cells of single-layer PtN 2 used to construct the nanotubes. Our work shows that dimension engineering of PtN 2 not only leads to a more stable 3D structure but also to 1D materials with novel properties.