One of the major themes of the modern condensed matter physics is the study of materials with nontrivial electronic structure topology. Particularly significant progress in this field has happened within the last decade, due to the discovery of topologically nontrivial states of matter, that have a gap in their energy spectrum, namely Topological Insulators and Topological Superconductors. In this talk I will describe the most recent work, partly my own, extending the notions of the nontrivial electronic structure topology to gapless states of matter as well, namely to semimetals and even metals. I will discuss both the theoretical concepts, and the recent experimental work, realizing these novel states of condensed matter.
