Stability of 2D Crystals from Tessellation

Abstract

AbstractReticular chemistry has been a cornerstone in the design of novel 2D materials. Despite numerous possibilities for topological arrangements, only a few with high symmetry can form stable networks. Here, starting from 2D carbons, four types of highly stable tessellations are discovered, which consist of chains of non‐hexagonal rings separated by hexagonal ribbons. A modified Read–Shockley model is established to perfectly describe the stability of these highly stable frameworks, which is based on the interaction between non‐hexagonal rings. Moreover, these four types of tessellations and the modified Read–Shockley model are found to be of general validity in designing highly stable 2D materials, which is verified by the calculations on polymorphs of boron nitride and molybdenum disulfide. Besides, among the studied 2D carbon allotropes, two semi‐metallic structures with highly anisotropic Dirac cones and one semimetal with a Dirac nodal line at the Fermi level are discovered, as protected by their D2h symmetry. Spin‐orbital coupling is further found to open small bandgaps for these three Dirac structures, making them nontrivial topological insulators. The in‐depth understanding of the stability of 2D crystals in this study provides a new way for rational design of 2D crystals that may show peculiar electronic structures.