Topological Crystallography
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Topological Crystallography
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Author : Toshikazu Sunada
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-23
Topological Crystallography written by Toshikazu Sunada and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-23 with Mathematics categories.
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.
Structural Crystallography Of Inorganic Oxysalts
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Author : Sergey V. Krivovichev
language : en
Publisher: OUP Oxford
Release Date : 2009-01-22
Structural Crystallography Of Inorganic Oxysalts written by Sergey V. Krivovichev and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-22 with Science categories.
This book is the first book dealing with structural crystallography of inorganic oxysalts in general. A special emphasis is placed upon structural topology and methods of its description. The latter include graph theory, nets, 2-D and 3-D tilings, polyhedra, etc. The structures considered range from minerals to organically templated oxysalts, for all of which this book provides a unified approach to structure interpretation and classification. Most of the structures have been analysed from the proposed viewpoint for the first time and it has been shown that they possess the same topological genealogy and relationships, sometimes despite their obvious chemical differences. In order to expand the range of oxysalts considered, the book offers not only traditional schemes but also alternative approaches such as anion topologis, anion-centered polyhedra and cation arrays. As such, this book can be considered as a comprehensive introduction into the amazingly complex and diverse world of inorganic oxysalts.
Topological Insulators
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Author :
language : en
Publisher: Elsevier
Release Date : 2013-11-23
Topological Insulators written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-23 with Science categories.
Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field. Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old field. Whereas it was thought that all band insulators are essentially equivalent, the new theory predicts two distinct classes of band insulators in two spatial dimensions and 16 classes in three dimensions. These "topological" insulators exhibit a host of unusual physical properties, including topologically protected gapless surface states and exotic electromagnetic response, previously thought impossible in such systems. Within a short time, this new state of quantum matter, topological insulators, has been discovered experimentally both in 2D thin film structures and in 3D crystals and alloys. It appears that topological insulators are quite common in nature, and there are dozens of confirmed substances that exhibit this behavior. Theoretical and experimental studies of these materials are ongoing with the goal of attaining the fundamental understanding and exploiting them in future practical applications. Usable as a textbook for graduate students and as a reference resource for professionals Includes the most recent discoveries and visions for future technological applications All authors are prominent in the field
Chemical Topology
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Author : Danail Bonchev
language : en
Publisher: CRC Press
Release Date : 2000-07-06
Chemical Topology written by Danail Bonchev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-06 with Science categories.
Topology has been extensively applied in the study of chemically linked and knotted structures, and also in the study of many biologically significant molecules such as proteins and DNA. These are the themes that are addressed in this volume of the Mathematical Chemistry series. The topological chirality of knotted and linked molecular species and the invariants that may characterize them are explored in detail.
Topological Structures In Ferroic Materials
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Author : Jan Seidel
language : en
Publisher: Springer
Release Date : 2016-02-12
Topological Structures In Ferroic Materials written by Jan Seidel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-12 with Science categories.
This book provides a state-of-the art overview of a highly interesting emerging research field in solid state physics/nanomaterials science, topological structures in ferroic materials. Topological structures in ferroic materials have received strongly increasing attention in the last few years. Such structures include domain walls, skyrmions and vortices, which can form in ferroelectric, magnetic, ferroelastic or multiferroic materials. These topological structures can have completely different properties from the bulk material they form in. They also can be controlled by external fields (electrical, magnetic, strain) or currents, which makes them interesting from a fundamental research point of view as well as for potential novel nanomaterials applications. To provide a comprehensive overview, international leading researches in these fields contributed review-like chapters about their own work and the work of other researchers to provide a current view of this highly interesting topic.
Topological Insulators
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Author : C.L. Kane
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-11-23
Topological Insulators written by C.L. Kane and has been published by Elsevier Inc. Chapters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-23 with Science categories.
We give a pedagogical introduction to theory of topological insulators. Following an introduction to the role of topology in band theory, we discuss several examples in detail. These include theories of the electric polarization in one dimension, the integer quantum Hall effect in two dimensions and topological insulators in two and three dimensions. We close with a brief discussion of topological crystalline insulators, nodal semimetals, topological superconductivity and topological defects.
Topological Insulators
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Author : Chaoxing Liu
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-11-23
Topological Insulators written by Chaoxing Liu and has been published by Elsevier Inc. Chapters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-23 with Science categories.
In the chapter, we review two proto-type models of topological insulators, namely the Bernevig-Hughes-Zhang model for HgTe quantum wells and the four band model for family of materials. Based on these two simple models, we discuss helical edge/surface states of topological insulators, as well as their exotic physical properties, including total angular momentum, spin and orbital textures, topological stability, and topological response of the surface states. Moreover, we summarize the basic principle to search for topological insulators from these two models and discuss the related topological materials.
Highlights In Mineralogical Crystallography
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Author : Thomas Armbruster
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-11-13
Highlights In Mineralogical Crystallography written by Thomas Armbruster and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-13 with Science categories.
"Highlights in Mineralogical Crystallography" presents a collection of review articles with the common topic: structural properties of minerals and synthetic analogues. It is a valuable resource for mineralogists, materials scientists, crystallographers, and earth scientists. This book includes: An introduction to the RRUFF database for structural, spectroscopic, and chemical mineral identification. A systematic evaluation of structural complexity of minerals. ab initio computer modelling of mineral surfaces. Natural quasicrystals of meteoritic origin. The potential role of terrestrial ringwoodite on the water content of the Earth's mantle. Structural characterization of nanocrystalline bio-related minerals by electron-diffraction tomography. The uniqueness of mayenite-type compounds as minerals and high-tech ceramics.
Topological Insulators
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Author : Ari M. Turner
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-11-23
Topological Insulators written by Ari M. Turner and has been published by Elsevier Inc. Chapters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-23 with Science categories.
Trivalent Discrete Surfaces And Carbon Structures
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Author : Hisashi Naito
language : en
Publisher: Springer
Release Date : 2023-11-21
Trivalent Discrete Surfaces And Carbon Structures written by Hisashi Naito and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-21 with Mathematics categories.
This book discusses discrete geometric analysis, especially topological crystallography and discrete surface theory for trivalent discrete surfaces. Topological crystallography, based on graph theory, provides the most symmetric structure among given combinatorial structures by using the variational principle, and it can reproduce crystal structures existing in nature. In this regard, the topological crystallography founded by Kotani and Sunada is explained by using many examples. Carbon structures such as fullerenes are considered as trivalent discrete surfaces from the viewpoint of discrete geometric analysis. Discrete surface theories usually have been considered discretization of smooth surfaces. Here, consideration is given to discrete surfaces modeled by crystal/molecular structures, which are essentially discrete objects.