Dirac Matter

This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describesthe surprising resurgence, as a low-energy effective theory of conducting electronsin many condensed matter systems, including graphene and topological insulators,of the famous equation originally invented by P.A.M. Dirac for relativistic quantum mechanics. In five highly pedagogical articles, as befits their origin in lectures to abroad scientific audience, this book explains why Dirac matters.Highlights include the detailed "Graphene and Relativistic Quantum Physics",written by the experimental pioneer, Philip Kim, and devoted to graphene, a form of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in2004-2005 by the future Nobel prize winners Kostya Novoselov and Andre Geim tothe so-called relativistic quantum Hall effect; the review entitled "Dirac Fermions inCondensed Matter and Beyond", written by two prominent theoreticians, Mark Goerbig and Gilles Montambaux, who consider many other materials than graphene,collectively known as "Dirac matter", and offer a thorough description of the mergingtransition of Dirac cones that occurs in the energy spectrum, in various experimentsinvolving stretching of the microscopic hexagonal lattice; the third contribution, entitled"Quantum Transport in Graphene: Impurity Scattering as a Probe of the Dirac Spectrum", given by Hélène Bouchiat, a leading experimentalist in mesoscopicphysics, with Sophie Guéron and Chuan Li, shows how measuring electrical transport,in particular magneto-transport in real graphene devices - contaminated byimpurities and hence exhibiting a diffusive regime - allows one to deeply probe theDirac nature of electrons. The last two contributions focus on topological insulators;in the authoritative "Experimental Signatures of Topological Insulators", LaurentLévy reviews recent experimental progress in the physics of mercury-telluride samplesunder strain, which demonstrates that the surface of a three-dimensional topologicalinsulator hosts a two-dimensional massless Dirac metal; the illuminating finalcontribution by David Carpentier, entitled "Topology of Bands in Solids: FromInsulators to Dirac Matter", provides a geometric description of Bloch wave functionsin terms of Berry phases and parallel transport, and of their topological classificationin terms of invariants such as Chern numbers, and ends with a perspective onthree-dimensional semi-metals as described by the Weyl equation.This book will be of broad general interest to physicists, mathematicians, andhistorians of science.