Theoretical and Experimental Study of Topological Invariants in Topological Crystalline Insulators PDF Download

Author: Juan Sebastián Calderón García
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
The topological crystalline Insulators (TCI) are topological materials with metallic surface states protected by a symmetry given by the crystalline structure, and not by the Time reversal one as in the usual topological insulators. These insulators, whose band structures are classified by new topological invariants, are the counterpart of the topological insulators but without the spin-orbit coupling being the principal aspect. In this work, a theoretical study on the present topological invariants is shown by means of experimental measurements in monocrystals of (Pb1-xSnx)Te which are grown for this project. Particularly, it is desired to understand the evolution with magnetic field of the Landau energy levels of this kind of topological insulators.

Author:
Publisher: Elsevier
ISBN: 0444633189
Category : Science
Languages : en
Pages : 349

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Book Description
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

Author: C.L. Kane
Publisher: Elsevier Inc. Chapters
ISBN: 0128086823
Category : Science
Languages : en
Pages : 42

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Book Description
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.

Author: Michael I. Monastyrsky
Publisher: Springer Science & Business Media
ISBN: 3540312641
Category : Science
Languages : en
Pages : 263

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Book Description
This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

Author: Huixia Luo
Publisher: John Wiley & Sons
ISBN: 1119407338
Category : Technology & Engineering
Languages : en
Pages : 416

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Book Description
This book is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for researchers and graduate students preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with the fundamental description on the topological phases of matter such as one, two- and three-dimensional topological insulators, and methods and tools for topological material's investigations, topological insulators for advanced optoelectronic devices, topological superconductors, saturable absorber and in plasmonic devices. Advanced Topological Insulators provides researchers and graduate students with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.

Author: Naoto Nagaosa
Publisher: Elsevier Inc. Chapters
ISBN: 0128086912
Category : Science
Languages : en
Pages : 39

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Book Description
The discovery of the rich topological structures of electronic states in solids has opened up many interesting possibilities. The “twist” of the wavefunctions in momentum space, which is characterized by topological invariants, leads to the robust edge or surface states. The electron fractionalization associated with these topological states brings about the novel physics such as absence of localization, topological magneto-electric effect, and Majorana fermions. Here we describe the principles and some concrete examples of the theoretical design of the topological materials and their functions based on these recent developments.

Author: Joel E. Moore
Publisher: Elsevier Inc. Chapters
ISBN: 0128086831
Category : Science
Languages : en
Pages : 31

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Book Description
The theory of the topological insulator phase that emerges via spin-orbit coupling in three-dimensional materials is introduced, stressing its relationship to earlier topological phases in two dimensions. An unusual surface state with an odd number of “Dirac points” appears as a consequence of bulk topological invariants of the band structure. A different theoretical approach is then presented, based on the Berry phase of Bloch electrons, in order to illustrate a deep connection to the orbital contribution to the magnetoelectric polarizability in all materials. The unique features of transport in the topological insulator surface state are reviewed with an emphasis on possible experiments. The final section discusses briefly connections to interacting phases including topological superconductors and some recent efforts to construct fractional topological insulators in three dimensions.

Author: János K. Asbóth
Publisher: Springer
ISBN: 3319256076
Category : Science
Languages : en
Pages : 176

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Book Description
This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.

Author: B. Andrei Bernevig
Publisher: Princeton University Press
ISBN: 069115175X
Category : Science
Languages : en
Pages : 259

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Book Description
This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.

Author: Joseph Maciejko
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 242

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Book Description
This dissertation brings together a number of topics in the theory of time-reversal invariant topological insulators. The first four chapters are devoted to the transport properties of the two-dimensional (2D) quantum spin Hall state. We explain nonlocal transport measurements in mercury telluride (HgTe) quantum wells in terms of a Landauer-Büttiker theory of helical edge transport and confirm the discovery of the quantum spin Hall state in this material. We find that decoherence can lead to backscattering without breaking microscopic time-reversal symmetry. As an example of incoherent scattering, we study a Kondo impurity in an interacting helical edge liquid. A renormalization group analysis shows the existence of an impurity quantum phase transition governed by the Luttinger parameter of the edge liquid between a local helical Fermi liquid with T^6 scaling of the low-temperature conductance, and an insulating strongly correlated phase with fractionally charged emergent excitations. In the presence of a time-reversal symmetry breaking magnetic field, it is known that even coherent scattering can lead to backscattering. Through exact numerical diagonalization we find that nonmagnetic quenched disorder has a strong localizing effect on the edge transport if the disorder strength is comparable to the bulk gap. The predicted magnetoconductance agrees qualitatively with experiment. The last two chapters are devoted to 3D topological insulators. We propose a combined magnetooptical Kerr and Faraday rotation experiment as a universal measure of the Z_2 invariant. Finally, we propose a fractional generalization of 3D topological insulators in strongly correlated systems, characterized by ground state degeneracy on topologically nontrivial spatial 3-manifolds, a quantized fractional bulk magnetoelectric polarizability without time-reversal symmetry breaking, and a halved fractional quantum Hall effect on the surface.