Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals

Understanding Dirac-like Fermions has become an imperative in modern condensed matter sciences: all across its research frontier, from graphene to high T$_c$ superconductors to the topological insulators and beyond, various electronic systems exhibit properties which can be well described by the Dirac equation. Such physics is no longer the exclusive domain of quantum field theories and other esoteric mathematical musings; instead, real physics of real systems is governed by such equations, and important materials science and practical implications hinge on our understanding of Dirac particles in two and three dimensions. While the physics that gives rise to the massless Dirac Fermions in each of the above mentioned materials is different, the low energy properties are governed by the same Dirac kinematics. The aim of this article is to review a selected cross-section of this vast field by highlighting the generalities, and contrasting the specifics, of several physical systems.