Thorny Road to Topological Insulators and Weyl Semimetals
The recent discovery of the novel materials - Weyl semimetals in 2015 completely changed our views on matter. I will describe a thorny historical way which lead to this discovery. I will discuss the main physical properties of Weyl semimetals and compare them with various topological insulators as well as two- dimensional crystals such as graphene, silicene, germanene and compare them with those of poly- acetylene. We comment on the origin of their buckled two-dimensional shape and draw their analogy with the Peierls distortions in polyacetylene. We also address the issues created by the Mermin-Wagner theorem prohibiting the existence of strictly two-dimensional crystals. Then we describe the main ideas which led to the discovery of topological insulators and Weyl semimetals and comment on a formation of Majorana fermions in these systems. We describe some of the outstanding electronic properties originate due to the breaking of fundamental symmetries as well as an existence of the Dirac and Weyl gapless spectra. The issues associated with Fermi arc in Weyl semimetals will be described. I will also compare properties of simplest devices made of Weyl semimetals and Dirac materials. Analogies and differences between Dirac materials, Weyl semimetals and optics will be also discussed.