December 4, 2020

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Topological Insulators and Topological Superconductors

Topological Insulators and Topological Superconductors
Author : B. Andrei Bernevig,Taylor L. Hughes
Publisher : Princeton University Press
Release Date : 2013-04-07
Category : Science
Total pages :247
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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.

Topological Insulators

Topological Insulators
Author : Frank Ortmann,Stephan Roche,Sergio O. Valenzuela
Publisher : John Wiley & Sons
Release Date : 2015-04-07
Category : Technology & Engineering
Total pages :432
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There are only few discoveries and new technologies in physical sciences that have the potential to dramatically alter and revolutionize our electronic world. Topological insulators are one of them. The present book for the first time provides a full overview and in-depth knowledge about this hot topic in materials science and condensed matter physics. Techniques such as angle-resolved photoemission spectrometry (ARPES), advanced solid-state Nuclear Magnetic Resonance (NMR) or scanning-tunnel microscopy (STM) together with key principles of topological insulators such as spin-locked electronic states, the Dirac point, quantum Hall effects and Majorana fermions are illuminated in individual chapters and are described in a clear and logical form. Written by an international team of experts, many of them directly involved in the very first discovery of topological insulators, the book provides the readers with the knowledge they need to understand the electronic behavior of these unique materials. Being more than a reference work, this book is essential for newcomers and advanced researchers working in the field of topological insulators.

Topological Insulators

Topological Insulators
Author : Ari M. Turner,Ashvin Vishwanath
Publisher : Elsevier Inc. Chapters
Release Date : 2013-11-23
Category : Science
Total pages :352
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Topological Insulators

Topological Insulators
Author : Panagiotis Kotetes
Publisher : Morgan & Claypool Publishers
Release Date : 2019-04-24
Category : Science
Total pages :215
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This book provides an introduction to topological matter with a focus on insulating bulk systems. A number of prerequisite concepts and tools are first laid out, including the notion of symmetry transformations, the band theory of semiconductors and aspects of electronic transport. The main part of the book discusses realistic models for both time-reversal-preserving and -violating topological insulators, as well as their characteristic responses to external perturbations. Special emphasis is given to the study of the anomalous electric, thermal, and thermoelectric transport properties, the theory of orbital magnetisation, and the polar Kerr effect. The topological models studied throughout this book become unified and generalised by means of the tenfold topological-classification framework and the respective systematic construction of topological invariants. This approach is further extended to topological superconductors and topological semimetals. This book covers a wide range of topics and aims at the transparent presentation of the technical aspects involved. For this purpose, homework problems are also provided in dedicated Hands-on sections. Given its structure and the required background level of the reader, this book is particularly recommended for graduate students or researchers who are new to the field.

Topological Insulators

Topological Insulators
Author : C.L. Kane
Publisher : Elsevier Inc. Chapters
Release Date : 2013-11-23
Category : Science
Total pages :352
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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

Topological Insulators
Author : Chaoxing Liu,Shoucheng Zhang
Publisher : Elsevier Inc. Chapters
Release Date : 2013-11-23
Category : Science
Total pages :352
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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.

Topological Insulators

Topological Insulators
Author : Gregory Tkachov
Publisher : CRC Press
Release Date : 2015-10-14
Category : Science
Total pages :182
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This book is the result of dynamic developments that have occurred in condensed matter physics after the recent discovery of a new class of electronic materials: topological insulators. A topological insulator is a material that behaves as a band insulator in its interior, while acting as a metallic conductor at its surface. The surface current carriers in these systems have Dirac-like nature and are protected by an intrinsic topological order, which is of great interest for both fundamental research and emerging technologies, especially in the fields of electronics, spintronics, and quantum information. The realization of the application potential of topological insulators requires a comprehensive and deep understanding of transport processes in these novel materials. This book explores the origin of the protected Dirac-like states in topological insulators and gives an insight into some of their representative transport properties. These include the quantum spin–Hall effect, nonlocal edge transport, backscattering of helical edge and surface states, weak antilocalization, unconventional triplet p-wave superconductivity, topological bound states, and emergent Majorana fermions in Josephson junctions as well as superconducting Klein tunneling.

Topological Insulators

Topological Insulators
Author : Xiao-Liang Qi
Publisher : Elsevier Inc. Chapters
Release Date : 2013-11-23
Category : Science
Total pages :352
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In this chapter we provide an overview of the topological field theory approach to topological insulators. We start by reviewing the topological field theory description of integer quantum Hall states, which also illustrates the general features of topological field theory approach. Then we reviewed the topological field theory approach of three-dimensional topological insulators and its physical consequences. In the last part of this section we discuss the generalizations of topological field theory approach to generic dimensions and other topological states of matter.

Topological Insulators

Topological Insulators
Author : Shun-Qing Shen
Publisher : Springer
Release Date : 2017-08-18
Category : Technology & Engineering
Total pages :266
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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.

Topological Insulators

Topological Insulators
Author : Vadim Nemytov
Publisher : Unknown
Release Date : 2013
Category :
Total pages :129
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"In this thesis we investigate quantum transport properties of topological insulator (TI) Bi2 Se3 from atomistic point of view. TI is a material having an energy gap in its bulk but supporting gapless helical states on its boundary. The helical states have Dirac-like linear energy dispersion continuously crossing the bulk band gap with a spin texture in which the electron spin is locked perpendicular to the electron momentum. The peculiar electronic structure of TI material Bi2 Se3 is due to a strong spin-orbit interaction and is protected by the time reversal symmetry. The thesis consists of two main parts. The first reviews the theory of TI and the second presents our atomistic calculations of electron transport in the Bi2 Se3 material. In the theoretical review of the physics of TI, I follow the literature and attempt to present it in a reasonably accessible manner. The theory of TI is explained in terms of well known physical phenomena including classical and quantum Hall effects, spin-orbit coupling, spin current, and spin-Hall effect. The concept of Berry's phase is then introduced to link with the formal conventionalclassification of TI by the topological Z2 invariants. The entire discussion is within the well known Bloch band theory. In the second part of this thesis, numerical studies of transport properties of Bi2 Se3 are presented. After a brief discussion of the relevant quantum transport theory and the tight binding atomistic model, we present our calculated quantum transport results of Bi2 Se3 films having a trench in the middle. Such a large defect, if on normal conductors, would cause significant back scattering of the carriers. Here, by topological protection of the helical states, back scattering is forbidden due to the spin-momentum locking. Nevertheless, large trenches in the film may cause the helical states on the surface to mix inside the trench, thereby affecting the transmission." --

Topological Insulators

Topological Insulators
Author : Joel E. Moore
Publisher : Elsevier Inc. Chapters
Release Date : 2013-11-23
Category : Science
Total pages :352
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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.

Topological Insulators

Topological Insulators
Author : Naoto Nagaosa
Publisher : Elsevier Inc. Chapters
Release Date : 2013-11-23
Category : Science
Total pages :352
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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.

Optical Properties of Bismuth-Based Topological Insulators

Optical Properties of Bismuth-Based Topological Insulators
Author : Paola Di Pietro
Publisher : Springer Science & Business Media
Release Date : 2013-10-24
Category : Technology & Engineering
Total pages :119
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Topological Insulators (TIs) are insulators in the bulk, but have exotic metallic states at their surfaces. The topology, associated with the electronic wavefunctions of these systems, changes when passing from the bulk to the surface. This work studies, by means of infrared spectroscopy, the low energy optical conductivity of Bismuth based TIs in order to identify the extrinsic charge contribution of the bulk and to separate it from the intrinsic contribution of the surface state carriers. The extensive results presented in this thesis definitely shows the 2D character of the carriers in Bismuth-based topological insulators. The experimental apparatus and the FTIR technique, the theory of optical properties and Surface Plasmon Polaritons, as well as sample preparation of both crystals and thin films, and the analysis procedures are thoroughly described.

Studies on Time-reversal Invariant Topological Insulators

Studies on Time-reversal Invariant Topological Insulators
Author : Anonim
Publisher : Stanford University
Release Date : 2011
Category :
Total pages :129
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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.

Topological Insulators

Topological Insulators
Author : Haim Beindenkopf,Pedram Roushan,Ali Yazdani
Publisher : Elsevier Inc. Chapters
Release Date : 2013-11-23
Category : Science
Total pages :352
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Topological insulators are materials in which spin-orbit coupling is strong enough as to invert the ordering of bulk bands about the insulating bulk gap. While the bulk properties of these materials are not much different than any other insulating material their topological classification ensures the existence of exotic states on their surfaces. These surface electrons behave as massless relativistic particles obeying Dirac dynamics which locks their spin degree of freedom to their momentum thus reducing by half their phase space relative to any other fermionic state. Furthermore, the helical spin-texture associated with their Dirac nature greatly restricts scattering of surface states as long as time-reversal symmetry is preserved. In particular it forbids backscattering and therefore immunes the topological surface electrons from localizing. Scanning tunneling microscopy (STM) and spectroscopic mappings have played a key role in the characterization of these unique properties of the topological surface states. By visualizing electronic standing wave patterns next to impurities it was verified that the helical surface states do not backscatter. On the other hand, the Dirac electrons were found to be susceptible to the electrostatic charging of these scaterres, which induce spatial fluctuation of the Dirac energy and spectrum. Nevertheless, the unusual resilience of the helical surface states to disorder was strikingly demonstrated by measuring their high transmittance in an atomic-scale Fabry-Perot interferometry set up. The latter is a consequence of the existence of the topological surface states on all surface terminations which stems directly from the bulk topological classification. In the following chapter these insightful contributions of STM to the field of topological insulators will be discussed in detail alongside with future directions.