This 15th quantity of the Poincare Seminar sequence, Dirac subject, describes the amazing resurgence, as a low-energy potent thought of undertaking electrons in many condensed topic platforms, together with graphene and topological insulators, of the recognized equation initially invented by means of P.A.M. Dirac for relativistic quantum

mechanics. In 5 hugely pedagogical articles, as befits their starting place in lectures to a broad medical viewers, this e-book explains why Dirac matters. Highlights comprise the targeted "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 via the long run Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum corridor influence; the overview entitled "Dirac Fermions in Condensed subject and Beyond", written by way of trendy theoreticians, Mark Goerbig and Gilles Montambaux, who contemplate many different fabrics than graphene, collectively often called "Dirac matter", and provide a radical description of the merging transition of Dirac cones that happens within the power spectrum, in a number 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 for this reason displaying 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 experiences contemporary experimental growth within the physics of mercury-telluride samples under pressure, which demonstrates that the skin of a 3-dimensional topological insulator hosts a two-dimensional massless Dirac steel; the illuminating final contribution through David Carpentier, entitled "Topology of Bands in Solids: From Insulators to Dirac Matter", offers a geometrical description of Bloch wave functions in phrases of Berry levels and parallel shipping, and in their topological classification in phrases of invariants corresponding to Chern numbers, and ends with a viewpoint on three-dimensional semi-metals as defined via the Weyl equation. This e-book may be of wide basic curiosity to physicists, mathematicians, and historians of science.