This 15th quantity of the Poincare Seminar sequence, Dirac topic, describes the dazzling resurgence, as a low-energy powerful thought of engaging in electrons in many condensed subject platforms, together with graphene and topological insulators, of the well-known equation initially invented by way of P.A.M. Dirac for relativistic quantum
mechanics. In 5 hugely pedagogical articles, as befits their beginning in lectures to a broad medical viewers, this booklet explains why Dirac matters. Highlights contain the specific "Graphene and Relativistic Quantum Physics", written by way of 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 by means of the longer term Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum corridor influence; the evaluation entitled "Dirac Fermions in Condensed topic and Beyond", written by way of trendy theoreticians, Mark Goerbig and Gilles Montambaux, who contemplate many different fabrics than graphene, collectively referred to as "Dirac matter", and provide a radical description of the merging transition of Dirac cones that happens within the strength spectrum, in quite a few 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 by way of 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 actual graphene units - infected by impurities and as a result 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 stories contemporary experimental growth within the physics of mercury-telluride samples under pressure, which demonstrates that the outside of a third-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", 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 similar to Chern numbers, and ends with a standpoint on three-dimensional semi-metals as defined by means of the Weyl equation. This booklet may be of wide basic curiosity to physicists, mathematicians, and historians of science.