Eur. Phys. J. B (2014) 87: 67
https://doi.org/10.1140/epjb/e2014-40894-9

Regular Article

Anisotropic Dirac cones in monoatomic hexagonal lattices: a DFT study

Departamento de Física, Universidad Nacional de Colombia, Ciudad Universitaria, 111321 Bogotá D.C., Colombia

^a e-mail: rrreyg@unal.edu.co

Received: 7 October 2013
Received in final form: 5 February 2014
Published online: 19 March 2014

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 D₃) 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.