This fifteenth volume of the Poincare Seminar Series, Dirac Matter,
describes the surprising resurgence, as a low-energy effective
theory of conducting electrons in 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 a broad 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 in 2004-2005 by the future Nobel prize winners Kostya
Novoselov and Andre Geim to the so-called relativistic quantum Hall
effect; the review entitled "Dirac Fermions in Condensed 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 merging transition of Dirac cones that occurs in
the energy spectrum, in various experiments involving 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 Helene Bouchiat, a leading
experimentalist in mesoscopic physics, with Sophie Gueron and Chuan
Li, shows how measuring electrical transport, in particular
magneto-transport in real graphene devices - contaminated by
impurities and hence exhibiting a diffusive regime - allows one to
deeply probe the Dirac nature of electrons. The last two
contributions focus on topological insulators; in the authoritative
"Experimental Signatures of Topological Insulators", Laurent Levy
reviews recent experimental progress in the physics of
mercury-telluride samples under strain, which demonstrates that the
surface of a three-dimensional topological insulator hosts a
two-dimensional massless Dirac metal; the illuminating final
contribution by David Carpentier, entitled "Topology of Bands in
Solids: From Insulators to Dirac Matter", provides a geometric
description of Bloch wave functions in terms of Berry phases and
parallel transport, and of their topological classification in
terms of invariants such as Chern numbers, and ends with a
perspective on three-dimensional semi-metals as described by the
Weyl equation. This book will be of broad general interest to
physicists, mathematicians, and historians of science.
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