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 the research frontier, from graphene to high T-c superconductors to the topological insulators and beyond, various electronic systems exhibit properties that 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, physics of real condensed matter 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. Although 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.