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Author: Bertrand Duplantier
Publisher: Birkhäuser
ISBN: 3319325361
Category : Science
Languages : en
Pages : 129
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Book Description
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 Hélène Bouchiat, a leading experimentalist in mesoscopic physics, with Sophie Guéron 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 Lévy 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.
Author: Bertrand Duplantier
Publisher: Birkhäuser
ISBN: 3319325361
Category : Science
Languages : en
Pages : 129
Get Book
Book Description
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 Hélène Bouchiat, a leading experimentalist in mesoscopic physics, with Sophie Guéron 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 Lévy 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.
Author: Shun-Qing Shen
Publisher: Springer Science & Business Media
ISBN: 364232858X
Category : Technology & Engineering
Languages : en
Pages : 234
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Book Description
Topological insulators are insulating in the bulk, but process metallic states present around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, the first of its kind on topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological insulators and related areas. Shun-Qing Shen is a Professor at the Department of Physics, the University of Hong Kong, China.
Author: Eduard V Gorbar
Publisher: World Scientific
ISBN: 9811207364
Category : Science
Languages : en
Pages : 535
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Book Description
The monograph reviews various aspects of electronic properties of Dirac and Weyl semimetals. After a brief discussion of 2D Dirac semimetals, a comprehensive review of 3D materials is given. The description starts from an overview of the topological properties and symmetries of Dirac and Weyl semimetals. In addition, several low-energy models of Dirac and Weyl quasiparticles are presented. The key ab initio approaches and material realizations are given. The monograph includes detailed discussions of the surface Fermi arcs, anomalous transport properties, and collective modes of Dirac and Weyl semimetals. Superconductivity in these materials is briefly addressed.
Author: Shun-Qing Shen
Publisher: Springer
ISBN: 9811046069
Category : Technology & Engineering
Languages : en
Pages : 266
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Book Description
This new edition presents a unified description of these insulators from one to three dimensions based on the modified Dirac equation. It derives a series of solutions of the bound states near the boundary, and describes the current status of these solutions. Readers are introduced to topological invariants and their applications to a variety of systems from one-dimensional polyacetylene, to two-dimensional quantum spin Hall effect and p-wave superconductors, three-dimensional topological insulators and superconductors or superfluids, and topological Weyl semimetals, helping them to better understand this fascinating field. To reflect research advances in topological insulators, several parts of the book have been updated for the second edition, including: Spin-Triplet Superconductors, Superconductivity in Doped Topological Insulators, Detection of Majorana Fermions and so on. In particular, the book features a new chapter on Weyl semimetals, a topic that has attracted considerable attention and has already become a new hotpot of research in the community.
Author: Laxman Raju Thoutam
Publisher: Springer Nature
ISBN: 9811913129
Category : Science
Languages : en
Pages : 472
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Book Description
This book serves as a quick guide on the latest material systems including their synthesis, fabrication and characterization techniques. It discusses recent developments in different material systems and discusses their novel applications in various branches of science and engineering. The book briefs latest computational tools and techniques that are used to discover new material systems. The book also briefs applications of new emerging materials in various fields including, healthcare, sensors, opto-electronics, high power devices and nano-electronics. This book helps to create a synergy between computational and experimental research methods to better understand a particular material system.
Author: Egor Babaev
Publisher: World Scientific
ISBN: 9811265070
Category : Science
Languages : en
Pages : 277
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Book Description
A geometric figure has chirality, or handedness, if its mirror image cannot be brought to coincide with itself. The concept of chirality was instrumental in establishing the tetrahedral valences of the carbon atom, and has continued to play a key role in chemistry and molecular biology ever since.The fact that living organisms use only one of two mirror isomers of such molecules as amino acids and sugars, that is, the question of the origin of homochirality of the molecular basis of life, remains an unsolved problem of the same dignity as the origin of dark matter and dark energy.The increasing importance of chirality and topology in condensed matter physics and chemistry, and the production of new states of matter in heavy-ion collisions, have brought the concept of chirality into physics and cosmology in a tangible way while at the same time expanded the physics/chemistry interface. The book is the first to address all aspects of chirality in a single volume.
Author: Kouki Yonaga
Publisher: Springer Nature
ISBN: 9811691665
Category : Science
Languages : en
Pages : 96
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Book Description
This book presents the high-precision analysis of ground states and low-energy excitations in fractional quantum Hall states formed by Dirac electrons, which have attracted a great deal of attention. In particular the author focuses on the physics of fractional quantum Hall states in graphene on a hexagonal boron nitride substrate, which was recently implemented in experiments. The numerical approach employed in the book, which uses an exact numerical diagonalization of an effective model Hamiltonian on a Haldane’s sphere based on pseudopotential representation of electron interaction, provides a better understanding of the recent experiments. The book reviews various aspects of quantum Hall effect: a brief history, recent experiments with graphene, and fundamental theories on integer and fractional Hall effects. It allows readers to quickly grasp the physics of quantum Hall states of Dirac fermions, and to catch up on latest research on the quantum Hall effect in graphene.
Author: Hiroki Isobe
Publisher: Springer
ISBN: 9811037434
Category : Technology & Engineering
Languages : en
Pages : 136
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Book Description
This thesis elucidates electron correlation effects in topological matter whose electronic states hold nontrivial topological properties robust against small perturbations. In addition to a comprehensive introduction to topological matter, this thesis provides a new perspective on correlated topological matter. The book comprises three subjects, in which electron correlations in different forms are considered. The first focuses on Coulomb interactions for massless Dirac fermions. Using a perturbative approach, the author reveals emergent Lorentz invariance in a low-energy limit and discusses how to probe the Lorentz invariance experimentally. The second subject aims to show a principle for synthesizing topological insulators with common, light elements. The interplay between the spin–orbit interaction and electron correlation is considered, and Hund's rule and electron filling are consequently found to play a key role for a strong spin–orbit interaction important for topological insulators. The last subject is classification of topological crystalline insulators in the presence of electron correlation. Unlike non-interacting topological insulators, such two- and three-dimensional correlated insulators with mirror symmetry are demonstrated to be characterized, respectively, by the Z4 and Z8 group by using the bosonization technique and a geometrical consideration.
Author: Steven M. Girvin
Publisher: Cambridge University Press
ISBN: 110713739X
Category : Science
Languages : en
Pages : 720
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Book Description
Comprehensive and accessible coverage from the basics to advanced topics in modern quantum condensed matter physics.
Author: Paulo André Dias Gonçalves
Publisher: Springer Nature
ISBN: 3030382915
Category : Science
Languages : en
Pages : 232
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Book Description
This thesis presents a comprehensive theoretical description of classical and quantum aspects of plasmonics in three and two dimensions, and also in transdimensional systems containing elements with different dimensionalities. It focuses on the theoretical understanding of the salient features of plasmons in nanosystems as well as on the multifaceted aspects of plasmon-enhanced light–matter interactions at the nanometer scale. Special emphasis is given to the modeling of nonclassical behavior across the transition regime bridging the classical and the quantum domains. The research presented in this dissertation provides useful tools for understanding surface plasmons in various two- and three-dimensional nanostructures, as well as quantum mechanical effects in their response and their joint impact on light–matter interactions at the extreme nanoscale. These contributions constitute novel and solid advancements in the research field of plasmonics and nanophotonics that will help guide future experimental investigations in the blossoming field of nanophotonics, and also facilitate the design of the next generation of truly nanoscale nanophotonic devices.
