This 15th quantity of the Poincare Seminar sequence, Dirac topic, describes the extraordinary resurgence, as a low-energy potent concept of undertaking electrons in many condensed subject structures, together with graphene and topological insulators, of the recognized equation initially invented by way of P.A.M. Dirac for relativistic quantum
mechanics. In 5 hugely pedagogical articles, as befits their foundation in lectures to a broad clinical viewers, this publication explains why Dirac matters. Highlights comprise the precise "Graphene and Relativistic Quantum Physics", written through the experimental pioneer, Philip Kim, and dedicated to graphene, a form
of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in 2004-2005 through the long run Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum corridor impression; the assessment entitled "Dirac Fermions in Condensed topic and Beyond", written via sought after theoreticians, Mark Goerbig and Gilles Montambaux, who give some thought to many different fabrics than graphene, collectively referred to as "Dirac matter", and provide an intensive description of the merging transition of Dirac cones that happens within the strength spectrum, in a variety of experiments involving stretching of the microscopic hexagonal lattice; the 3rd contribution, entitled "Quantum shipping in Graphene: Impurity Scattering as a Probe of the Dirac
Spectrum", given through Hélène Bouchiat, a number one experimentalist in mesoscopic physics, with Sophie Guéron and Chuan Li, indicates how measuring electric transport, in specific magneto-transport in genuine graphene units - infected by impurities and consequently showing a diffusive regime - permits one to deeply probe the Dirac nature of electrons. The final contributions concentrate on topological insulators; in the authoritative "Experimental Signatures of Topological Insulators", Laurent Lévy studies contemporary experimental development within the physics of mercury-telluride samples under pressure, which demonstrates that the skin of a three-d topological insulator hosts a two-dimensional massless Dirac steel; the illuminating final contribution via David Carpentier, entitled "Topology of Bands in Solids: From Insulators to Dirac Matter", presents a geometrical description of Bloch wave functions in phrases of Berry levels and parallel delivery, and in their topological classification in phrases of invariants equivalent to Chern numbers, and ends with a point of view on three-dimensional semi-metals as defined by means of the Weyl equation. This e-book should be of wide basic curiosity to physicists, mathematicians, and historians of science.