Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics, Prodan Emil, Schulz-Baldes Hermann

Автор: Valeri Ligatchev
Название: Mathematical & Physical Aspects of Experimental Investigations on Electron & Relaxation Time Spectra in Bulk & Nano-Structured Semiconductors & Insulators
ISBN: 1536125660 ISBN-13(EAN): 9781536125665
Издательство: Nova Science
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Описание: This book summarises important outcomes of a quarter century of developments in advanced mathematical approaches and their implementations for deconvolution. The analysis of electron and relaxation time spectra obtained from the results of appropriate physical experiments fulfilled on real samples of bulk amorphous/crystalline semiconductors and insulators as well as on nano-structured materials and devices are also discussed. The second chapter of this book depicts key features of many well-known traditional and some modern techniques for experimental investigations of electron density and time relaxation spectra in such semiconductors and insulators. as Additionally, there is an emphasis on archetypal problems related to the analysis and interpretation of the results of those experimental techniques. Some generic (though crucially important in the context of this book) physical and mathematical aspects of the polarisation and relaxation processes in solids, well-known one-dimensional direct and inverse integral transforms, linear integral equations of the first and second kinds, ill-posed mathematical problems and specific mathematical approaches to solution(s) of those are discussed in the third, fourth and fifth chapters, respectively. A majority of the aforementioned mathematical approaches are essentially based on the so-called regularisation concept, pioneered by famous Russian mathematicians (A N Tikhonov, M M Lavrentiev, V K Ivanov, V Ya Arsenin and their co-workers) in the second half of the twentieth century. Mathematical aspects of the regularisation concept are discussed (to some extent) in the fifth chapter of the book in comparison to the similar aspects of the traditional modelling approach with multiple references on appropriate original articles and books. Thanks to distinctive features of the regularisation concept, it endures a protracted history (which nowadays well exceeds 5 decades), becomes the dominant strategy for the solution of various inverse problems, and is widely used in many types of modern applications and computational packages. In particular, the regularisation algorithms are incorporated into Mathematica, Matlab, Python and Octave packages. This generic regularisation concept had been successfully implemented by the author of this book during the development and practical realisation (programming) of several essentially different regularisation algorithms (described in detail in the sixth chapter of the book) for unambiguous investigations and the analysis of results of appropriated physical experiments, fulfilled over a period from 1984 to 2009, both in Russia and in Singapore. Furthermore, actual results of such experimental investigations are discussed in the seventh chapter following closely appropriate original publications, and in comparison with their counterparts obtained by traditional (eg: modelling) approaches. As it is also demonstrated in the seventh chapter with the relevant examples and detailed discussion(s), the implementation of the aforementioned regularisation algorithms allows one to identify (and interpret thereafter) new important features of the intra-gap and near-band-gap electronic spectra of the amorphous and polycrystalline semiconductors and insulators. The relaxation time spectra of those materials, which are usually unattainable via the implementation of the modelling approach is also analysed. It is important that the regularisation concept (mathematically related to its alternative ones, e.g., the direct and inverse Radon integral transforms) has many other, very important implementations, e.g., in medical computerised tomography, security-related applications, archaeology, geophysics, etc. Similar to the abovementioned spectroscopic techniques, the X-ray-based computerised tomography eventually yields vital information on features of electron density distribution in a studied object, though the desired function in the latter case rather depends on spatial variables than on energetic ones. The mathematical essence of the Radon-transform-based computerised tomography is also summarised very briefly in one of the sections of this book. A comprehensive reference list of this book comprises many other key references (for those who are interested in the aforementioned topics discussed herein).

Автор: Marcel Franz
Название: Topological Insulators,6
ISBN: 0444633146 ISBN-13(EAN): 9780444633149
Издательство: Elsevier Science
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Описание: Describes the revolution in condensed matter physics that occurred in our understanding of crystalline solids. This book chronicles the work done worldwide that led to these discoveries and provides the reader with an overview of the field.

Автор: Howard
Название: Measuring, Interpreting and Translating Electron Quasiparticle - Phonon Interactions on the Surfaces of the Topological Insulators Bismuth Selenide and Bismuth Telluride
ISBN: 331944722X ISBN-13(EAN): 9783319447223
Издательство: Springer
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Цена: 104480.00 T
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Описание: The thesis presents experimental and theoretical results about the surface dynamics and the surface Dirac fermion (DF) spectral function of the strong topological insulators Bi2Te3 and Bi2Se3. The experimental results reveal the presence of a strong Kohn anomaly in the measured surface phonon dispersion of a low-lying optical mode, and the absence of surface Rayleigh acoustic phonons. Fitting the experimental data to theoretical models employing phonon Matsubara functions allowed the extraction of the matrix elements of the coupling Hamiltonian and the modifications to the surface phonon propagator that are encoded in the phonon self-energy. This allowed, for the first time, calculation of phonon mode-specific DF coupling ??(q) from experimental data, with average coupling significantly higher than typical values for metals, underscoring the strong coupling between optical surface phonons and surface DFs in topological insulators. Finally, to connect to experimental results obtained from photoemission spectroscopies, an electronic (DF) Matsubara function was constructed using the determined electron-phonon matrix elements and the optical phonon dispersion. This allowed calculation of the DF spectral function and density of states, allowing for comparison with photoemission and scanning tunneling spectroscopies. The results set the necessary energy resolution and extraction methodology for calculating ? from the DF perspective.

Автор: Emil Prodan
Название: A Computational Non-commutative Geometry Program for Disordered Topological Insulators
ISBN: 3319550225 ISBN-13(EAN): 9783319550220
Издательство: Springer
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Цена: 51230.00 T
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Описание: Disordered Topological Insulators: A Brief Introduction.- Homogeneous Materials.- Homogeneous Disordered Crystals.- Classification of Homogenous Disordered Crystals.- Electron Dynamics: Concrete Physical Models.- Notations and Conventions.- Physical Models.- Disorder Regimes.- Topological Invariants.- The Non-Commutative Brillouin Torus.- Disorder Configurations and Associated Dynamical Systems.- The Algebra of Covariant Physical Observables.- Fourier Calculus.- Differential Calculus.- Smooth Sub-Algebra.- Sobolev Spaces.- Magnetic Derivations.- Physics Formulas.- The Auxiliary C*-Algebras.- Periodic Disorder Configurations.- The Periodic Approximating Algebra.- Finite-Volume Disorder Configurations.- The Finite-Volume Approximating Algebra.- Approximate Differential Calculus.- Bloch Algebras.- Canonical Finite-Volume Algorithm.- General Picture.- Explicit Computer Implementation.- Error Bounds for Smooth Correlations.- Assumptions.- First Round of Approximations.- Second Round of Approximations.- Overall Error Bounds.- Applications: Transport Coefficients at Finite Temperature.- The Non-Commutative Kubo Formula.- The Integer Quantum Hall Effect.- Chern Insulators.- Error Bounds for Non-Smooth Correlations.- The Aizenman-Molchanov Bound.- Assumptions.- Derivation of Error Bounds.- Applications II: Topological Invariants.- Class AIII in d = 1.- Class A in d = 2.- Class AIII in d = 3.- References.

Автор: Vladimir G. Turaev
Название: Quantum Invariants of Knots and 3-Manifolds
ISBN: 3110442663 ISBN-13(EAN): 9783110442663
Издательство: Walter de Gruyter
Цена: 185890.00 T
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Описание: Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents:Invariants of graphs in Euclidean 3-space and of closed 3-manifoldsFoundations of topological quantum field theoryThree-dimensional topological quantum field theoryTwo-dimensional modular functors6j-symbolsSimplicial state sums on 3-manifoldsShadows of manifolds and state sums on shadowsConstructions of modular categories

Автор: Zhang Jinsong
Название: Transport Studies of the Electrical, Magnetic and Thermoelectric Properties of Topological Insulator Thin Films
ISBN: 3662570491 ISBN-13(EAN): 9783662570494
Издательство: Springer
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Цена: 93160.00 T
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Описание: This book presentsthe transport studies of topological insulator thin films grown by molecularbeam epitaxy. Through band structure engineering, the ideal topologicalinsulators, (Bi1 xSbx)2Te3 ternary alloys, are successfully fabricated, whichpossess truly insulating bulk and tunable conducting surface states.

Автор: Yasuda Kenji
Название: Emergent Transport Properties of Magnetic Topological Insulator Heterostructures
ISBN: 9811571821 ISBN-13(EAN): 9789811571824
Издательство: Springer
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Описание: This book reveals unique transport phenomena and functionalities in topological insulators coupled with magnetism and superconductivity.

Автор: M.V. Reyes S?nchez; A. Verschoren
Название: Classical and Involutive Invariants of Krull Domains
ISBN: 9401064946 ISBN-13(EAN): 9789401064941
Издательство: Springer
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Автор: Li Weiping
Название: Lecture Notes On Knot Invariants
ISBN: 9814675954 ISBN-13(EAN): 9789814675956
Издательство: World Scientific Publishing
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Цена: 65470.00 T
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Описание: The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry.

Автор: Emil Prodan; Hermann Schulz-Baldes
Название: Bulk and Boundary Invariants for Complex Topological Insulators
ISBN: 3319293508 ISBN-13(EAN): 9783319293509
Издательство: Springer
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Цена: 65210.00 T
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Описание: This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry.

Автор: Howard Colin
Название: Measuring, Interpreting and Translating Electron Quasiparticle - Phonon Interactions on the Surfaces of the Topological Insulators Bismuth Selenide an
ISBN: 3319831208 ISBN-13(EAN): 9783319831206
Издательство: Springer
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Цена: 124730.00 T
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Описание: The thesis presents experimental and theoretical results about the surface dynamics and the surface Dirac fermion (DF) spectral function of the strong topological insulators Bi2Te3 and Bi2Se3.

Автор: John D. Moore
Название: Lectures on Seiberg-Witten Invariants
ISBN: 3540412212 ISBN-13(EAN): 9783540412212
Издательство: Springer
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Цена: 32560.00 T
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Описание: An introduction to the theory of Seiberg-Witten invariants suitable for second-year graduate students. These invariants can be used to prove that there are many compact topological four-manifolds which have more than one smooth structure, and that others have no smooth structure at all.