2134/26726 Romilly D.Y. Hills Romilly D.Y. Hills Matej Brada Matej Brada Yang Liu Yang Liu Michael P. Pierpoint Michael P. Pierpoint Binoy Sobnack Binoy Sobnack Wai M. Wu Wai M. Wu Feodor Kusmartsev Feodor Kusmartsev From graphene and topological insulators to Weyl semimetals Loughborough University 2017 Graphene Silicene Germanene Phosphorene Topological insulator Weyl semimetal Dirac cone Transistor, Landauer formalism Physical Sciences not elsewhere classified 2017-09-28 13:19:54 Chapter https://repository.lboro.ac.uk/articles/chapter/From_graphene_and_topological_insulators_to_Weyl_semimetals/9411182 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, sil- icene, 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 exis- tence of strictly two-dimensional, at 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 di erences between Dirac materials and optics are also discussed.