# Dimension Engineering of Single-Layer PtN$_2$ with the Cairo Tessellation

## TL;DR

This paper explores the structural and electronic properties of single-layer PtN$_2$ with Cairo tessellation, proposing a new stable bulk structure, and investigates the potential for nanotube formation and property tuning through dimension engineering.

## Contribution

It introduces a novel tetrahedral layered bulk structure of PtN$_2$, more stable than known forms, and demonstrates the feasibility of creating and tuning PtN$_2$ nanotubes.

## Key findings

- The new bulk PtN$_2$ structure is more stable than pyrite and single-layer forms.
- PtN$_2$ nanotubes have tunable band gaps based on their construction.
- The energy required for nanotube formation is comparable to other 2D materials.

## Abstract

Single-layer PtN$_2$ 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 PtN$_2$ has also been predicted to show semiconducting behavior with direct band gaps. 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 tetrahedral 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 band gaps of PtN$_2$ nanotubes are tunable by changing the number of unit cells $N$ 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 1D materials with novel properties.