From Pentagonal Geometries to Two-Dimensional Materials

Most of the most popular two-dimensional (2D) materials, such as semiconducting MoS₂ and magnetic CrI₃, adopt hexagonal structures. Inspired by the geometries of the existing 15 types of convex pentagons that can tessellate a plane without creating a gap or overlap, we combined these pentagonal geometries and density functional theory (DFT) calculations to predict novel 2D materials. We showed that this combination leads to a new direction in the field of 2D materials. In particular, we discovered a hidden pattern of pentagons called the Cairo tessellation in a group of bulk materials with the pyrite structure. We predicted single-layer PtP₂ to exhibit a completely planar, pentagonal structure and a direct band gap. Our work shows that encoding quantum mechanics into pentagonal geometries and with the help of DFT calculations open up a novel route for accelerating discovery of new 2D materials.