Dirac Fermions in Graphene with Stacking Fault Induced Periodic Line Defects

A carbon allotrope with twisted Dirac cones induced by grain boundaries composed of pentagons and octagons

The grain boundaries (GBs) composed of pentagons and octagons (558 GBs) have been demonstrated to induce attractive transport properties such as Van Hove singularity (VHS) and quasi-one-dimensional metallic wires. Here, we propose a monolayer carbon allotrope which is formed from the introduction of periodic 558 GBs to decorate intact graphene, termed as PHO-graphene. The calculated electronic properties indicate that PHO-graphene not only inherits the previously superior characteristics such as Van Hove singularity and quasi-one-dimensional metallic wires, but also possesses two twisted Dirac cones near the Fermi level. Further calculation finds that the Berry phase is quantized to ± π at the two Dirac points, which is consistent with the distribution of the corresponding Berry curvature. The parity argument uncovers that PHO-graphene hosts a nontrivial band topology and the edge states connecting the two Dirac points are clearly visible. Our findings not only provide a reliable avenue to realize the abundant and extraordinary properties of carbon allotropes, but also offer an attractive approach for designing all carbon-based devices.

Dirac Fermions in the Boron Nitride Monolayer with a Tetragon

Two-dimensional (2D) boron nitride (BN) is a promising candidate for aerospace materials due to its excellent mechanical and thermal stability properties. However, its unusually prominent band gap limits its application prospects. In this work, we report a gapless monolayer BN, t-BN, which has four anisotropic Dirac cones in the first Brillouin zone exactly at the Fermi level. To further confirm the semimetallic character, the nontrivial topological properties are proven through the topologically protected edge states and the invariant non-zero Z₂. Additionally, the Young's modulus and Poisson ratio characterize the strong mechanical strength of t-BN. Our theoretical predictions provide more possibilities for exploring the Dirac cone in BN, which will enhance the 2D boron derivative materials.