From pentagonal geometries to two-dimensional materials

Hexagons are dominating building blocks in the atomic structures of existing and predicted two-dimensional (2D) materials. A wealth of properties possessed by numerous 2D materials are attributed to their hexagonal, structural units. Although many review articles exist for 2D hexagonal materials, this review focus on a less common building block, pentagon, of 2D materials. We start with introducing 15 types of convex pentagons that can tile an infinite plane without creating a gap. We connect one of these pentagonal geometries (type 2 pentagon) with 2D materials via density functional theory (DFT) calculations, resulting in predictions of 2D pentagonal materials that could be synthesized in experiments. We summarize the experimental and theoretical efforts in this burgeoning subfield of 2D materials research. We also suggest several issues that DFT calculations can continue to address to develop the subfield. We expect this brief review to stimulate further experimental and computational interests in synthesizing and designing new 2D pentagonal materials.