Tiling Phosphorene

TL;DR

This paper introduces a novel tiling scheme to categorize layered phosphorene structures, linking atomic arrangements to a 2D tiling pattern, and explores stability and electronic properties based on this mapping.

Contribution

It presents a new method to classify phosphorene allotropes using a 2D tiling pattern, enabling analysis of stability and electronic features across various structures.

Findings

Structural stability depends on the tiling pattern index N.

Electronic properties are primarily influenced by the structural index N.

The mapping approach applies to non-hexagonal and quasicrystalline phosphorene structures.

Abstract

We present a scheme to categorize the structure of different layered phosphorene allotropes by mapping their non-planar atomic structure onto a two-color 2D triangular tiling pattern. In the buckled structure of a phosphorene monolayer, we assign atoms in "top" positions to dark tiles and atoms in "bottom" positions to light tiles. Optimum $sp^3$ bonding is maintained throughout the structure when each triangular tile is surrounded by the same number $N$ of like-colored tiles, with $0{\le}N{\le}2$. Our ab initio density functional calculations indicate that both the relative stability and electronic properties depend primarily on the structural index $N$. The proposed mapping approach may also be applied to phosphorene structures with non-hexagonal rings and 2D quasicrystals with no translational symmetry, which we predict to be nearly as stable as the hexagonal network.