Anisotropic Dirac cones in monatomic hexagonal lattices

TL;DR

This paper investigates the electronic properties of monatomic hexagonal silicon and germanium layers, revealing the presence of anisotropic Dirac cones near the K points, which influence their Fermi velocities and stability.

Contribution

It provides the first theoretical evidence of stable h-Si and h-Ge monolayers exhibiting anisotropic Dirac cones, expanding the understanding of 2D materials beyond graphene.

Findings

Both h-Si and h-Ge are chemically stable.

Dirac cones with D3 symmetry are present near K points.

Fermi velocities vary significantly with direction.

Abstract

In the last few years, the fascinating properties of graphene have been thoroughly investigated. The existence of Dirac cones is the most important characteristic of the electronic band-structure of graphene. In this theoretical paper, hexagonal monolayers of silicon (h-Si) and germanium (h-Ge) are examined using density functional theory, within the generalized gradient approximation. Our numerical results indicate that both h-Si and h-Ge are chemically stable. The lattice parameters, electronic dispersion relations and densities of states for these systems are reported. The electronic dispersion relations display Dirac cones with the symmetry of an equilateral triangle (the group D$_3$) in the vicinity of the K points. Hence, the Fermi velocity depends on the wave vector direction around $K$ points. Fermi velocities for holes and electrons are significantly different. The maximum and minimum Fermi velocities are also reported.