Dimension engineering of single-layer PtN2 with the Cairo tessellation

Abstract

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.

Toward obtaining 2D and 3D and 1D PtPN with pentagonal pattern

“…It seems to be expected that the band gap of bulk PtPN lies between those of bulk PtN 2 and PtP 2 . This trend also holds as the HSE06 band gaps of bulk PtN 2 , PtPN, and PtP 2 are 2.22, 15 1.76, and 1.59 eV, 26 respectively. For the three materials, one common feature…”

“…As can be seen, it is semiconducting with an indirect band gap of 1.21 eV. Bulk PtN 2 and PtP 2 with the pyrite structure are also found to have indirect PBE band gaps of 1.35 15 and 1.06 eV, 26 respectively. It seems to be expected that the band gap of bulk PtPN lies between those of bulk PtN 2 and PtP 2 .…”

“…If assuming bulk PtN 2 also adopts the pyrite structure, we encounter an incorrect conclusion that single-layer PtN 2 is more stable than bulk PtN 2 with the pyrite structure. 15 We recently proposed a new structure of bulk PtN 2 with layered structure. We also compute the energy of bulk PtPN with a similar layered structure, but it is higher than that of bulk PtPN with the pyrite-type structure by 180 meV/atom, confirming that the latter structure is the most stable one.…”

“…is the decrease in their band gaps due to the dimension reduction-the PBE band gaps of single-layer PtN 2 and PtP 2 are so small that they should probably be regarded as metallic. 15 The PBE functional therefore not only underestimates the band gap of single-layer PtPN, but also performs poorly in determining the electronic structures (metallic or semiconducting) of single-layer PtN 2 and PtP 2 possibly due to their four-fold rotational symmetry, leading to the degenerate energy levels at the M point and at the Fermi level. By contrast, all the single-layer forms of these three systems have direct band gaps at the HSE06 hybrid density functional level of theory and the HSE06 band gap of single-layer PtPN no longer lies between those of single-layer PtN 2 and PtP 2 .…”

“…As two most promising examples, single-layer PtP 2 and PtN 2 [11][12][13][14] have been predicted to exhibit a unique planar, pentagonal structure and attractive electronic structures such as direct band gaps calculated at the level of hybrid density functional theory-note that the band gaps at the level of Perdew-Burke-Ernzerhof (PBE) functional theory are negligibly small. 12,15 But the stability of the bulk counterparts of these two single-layer pentagonal materials and their formation energies are likely to prohibit successful synthesis or exfoliation. In particular, bulk PtN 2 with the pyrite structure is stable only at high pressures.…”