From graphene and topological insulators to Weyl semimetals

Here we present a short introduction into physics of Dirac materials. In particular we review main physical properties of various two-dimensional crystals such as graphene, silicene, germanene and others. We comment on the origin of their buckled two-dimensional shape, and address the issues created by Mermin-Wagner theorem prohibiting the existence of strictly two-dimensional, flat crystals. Then we describe main ideas which were leading to the discovery of two and three-dimensional topological insulators and Weyl fermions. We describe some of their outstanding electronic properties which have been originating due to the existence of the Dirac gapless spectrum. We also compare simplest devices made of Dirac materials. Analogies and differences between Dirac materials and optics are also discussed.