Electronic structure of two-dimensional crystals from<i>ab initio</i>theory

We report on ab initio calculations of the two-dimensional systems ${\text{MoS}}_{2}$ and ${\text{NbSe}}_{2}$, which recently were synthesized. We find that two-dimensional ${\text{MoS}}_{2}$ is a semiconductor with a gap which is rather close to that of the three-dimensional analog, and that ${\text{NbSe}}_{2}$ is a metal, which is similar to the three-dimensional analog of this compound. We further computed the electronic structure of the two-dimensional hexagonal (graphene-like) lattices of Si and Ge and compared them with the electronic structure of graphene. It is found that the properties related to the Dirac cone do not appear in the case of two-dimensional hexagonal germanium, which is metallic, contrary to two-dimensional hexagonal silicon, also known as silicene, which has an electronic structure very similar to the one of graphene, making them possibly equivalent.