The Rare Two-Dimensional Materials with Dirac Cones

TL;DR

This paper reviews recent theoretical research on 2D materials with Dirac cones, explaining their rarity and providing insights into their structural and electronic properties, emergence, and conditions for Dirac points.

Contribution

It offers a comprehensive overview of various 2D Dirac materials, analyzing the factors influencing the presence of Dirac cones and applying the von Neumann-Wigner theorem for explanation.

Findings

Dirac cones are rare in 2D materials due to strict symmetry and parameter requirements.

Structural features significantly influence the emergence of Dirac points.

The von Neumann-Wigner theorem explains the scarcity of Dirac cones.

Abstract

Inspired by the great development of graphene, more and more works have been conducted to seek new two-dimensional (2D) materials with Dirac cones. Although 2D Dirac materials possess many novel properties and physics, they are rare compared with the numerous 2D materials. To provide explanation for the rarity of 2D Dirac materials as well as clues in searching for new Dirac systems, here we review the recent theoretical aspects of various 2D Dirac materials, including graphene, silicene, germanene, graphynes, several boron and carbon sheets, transition metal oxides (VO2)n/(TiO2)m and (CrO2)n/(TiO2)m, organic and organometallic crystals, so-MoS2, and artificial lattices (electron gases and ultracold atoms). Their structural and electronic properties are summarized. We also investigate how Dirac points emerge, move, and merge in these systems. The von Neumann-Wigner theorem is used to explain the scarcity of Dirac cones in 2D systems, which leads to rigorous requirements on the symmetry, parameters, Fermi level, and band overlap of materials to achieve Dirac cones. Connections between existence of Dirac cones and the structural features are also discussed.