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## Topological Insulators and Topological Superconductors

- Author : B. Andrei Bernevig,Taylor L. Hughes
- Publisher :Unknown
- Release Date :2013-04-07
- Total pages :247
- ISBN : 9780691151755

**Summary :** 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

- Author : Frank Ortmann,Stephan Roche,Sergio O. Valenzuela
- Publisher :Unknown
- Release Date :2015-04-07
- Total pages :432
- ISBN : 9783527681600

**Summary :** 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

- Author : Gregory Tkachov
- Publisher :Unknown
- Release Date :2015-10-14
- Total pages :182
- ISBN : 9789814613262

**Summary :** 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

- Author : Panagiotis Kotetes
- Publisher :Unknown
- Release Date :2019-04-24
- Total pages :215
- ISBN : 9781681745176

**Summary :** 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

- Author : Ari M. Turner,Ashvin Vishwanath
- Publisher :Unknown
- Release Date :2013-11-23
- Total pages :352
- ISBN : 9780128086926

**Summary :**

## Advanced Topological Insulators

- Author : Huixia Luo
- Publisher :Unknown
- Release Date :2019-03-12
- Total pages :400
- ISBN : 9781119407331

**Summary :** 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.

## Topological Insulators

- Author : C.L. Kane
- Publisher :Unknown
- Release Date :2013-11-23
- Total pages :352
- ISBN : 9780128086827

**Summary :** 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

- Author : Chaoxing Liu,Shoucheng Zhang
- Publisher :Unknown
- Release Date :2013-11-23
- Total pages :352
- ISBN : 9780128086841

**Summary :** 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.

## Magnetism in Topological Insulators

- Author : Vladimir Litvinov
- Publisher :Unknown
- Release Date :2019-05-07
- Total pages :158
- ISBN : 9783030120535

**Summary :** This book serves as a brief introduction to topological insulator physics and device applications. Particular attention is paid to the indirect exchange interaction mediated by near surface Dirac fermions and the spin texture this interaction favors. Along with useful information on semiconductor material systems, the book provides a theoretical background for most common concepts of TI physics. Readers will benefit from up to date information and methods needed to start working in TI physics, theory, experiment and device applications. Discusses inter-spin interaction via massless and massive Dirac excitations; Includes coverage of near-surface spin texture of the magnetic atoms as related to their mutual positions as well to their positions with respect to top and bottom surfaces in thin TI film; Describes non-RKKY oscillating inter-spin interaction as a signature of the topological state; Explains the origin of the giant Rashba interaction at quantum phase transition in TI-conventional semiconductors.

## A Short Course on Topological Insulators

- Author : János K. Asbóth,László Oroszlány,András Pályi Pályi
- Publisher :Unknown
- Release Date :2016-02-22
- Total pages :166
- ISBN : 9783319256078

**Summary :** 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.

## Topological Insulators

- Author : Shun-Qing Shen
- Publisher :Unknown
- Release Date :2013-01-11
- Total pages :225
- ISBN : 9783642328589

**Summary :** 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.

## Topological Insulators

- Author : Shun-Qing Shen
- Publisher :Unknown
- Release Date :2017-08-18
- Total pages :266
- ISBN : 9789811046063

**Summary :** 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

- Author : Vadim Nemytov
- Publisher :Unknown
- Release Date :2013
- Total pages :229
- ISBN : OCLC:921888696

**Summary :** "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

- Author : Haim Beindenkopf,Pedram Roushan,Ali Yazdani
- Publisher :Unknown
- Release Date :2013-11-23
- Total pages :352
- ISBN : 9780128086889

**Summary :** 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.

## Topological Insulators

- Author : Naoto Nagaosa
- Publisher :Unknown
- Release Date :2013-11-23
- Total pages :352
- ISBN : 9780128086919

**Summary :** 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.

## Photoemission Studies of Topological Insulators

- Author : Turgut Yilmaz
- Publisher :Unknown
- Release Date :2016
- Total pages :229
- ISBN : OCLC:1196360063

**Summary :** Ph.D. Dissertation Turgut Yilmaz Graduate Student UConn Department of Physics "Photoemission Studies of Topological Insulators" Topological insulators (TIs) attracted scientist due to its distinct electronic structure. TIs possess metallic surfaces due to strong spin orbit coupling, while the bulk shows the insulating behavior. On the surface of TIs topologically protected surface states by time reversal symmetry (TRS) obeys the massless Dirac equation. One of the interest on TIs is to introduce magnetic impurities into bulk and on the surface to break TRS leading to open an energy gap at the Dirac point of TIs. Therefore, x-ray photoemission spectroscopy (XPS) and angle resolved photoemission spectroscopy (ARPES) study on Cr bulk and surface doped Bi2Se3 were presented in order to investigate magnetic impurity doping impact on the electronic and chemical environment of Bi2Se3. ARPES measurements revealed that Cr bulk doping opens an energy gap at the Dirac point without ferromagnetism, while gapless surface states are robust against Cr surface deposition. Another interest on TIs is to obtain proximity induced superconductivity in order to open experimental avenue for possible experimental detection of Majorana fermions. Therefore, we presented ARPES study on Bi2Se3/ Bi2Sr2CaCu2O8+Î ́ (BSCCO) heterostructure in order to search for proximity induced superconductivity. In contrast to expectations, ARPES measurements do not show any sign of the proximity induced superconductivity in the thickness range from 0.5 quintuple layer of Bi2Se3 to 15 quintuple layer of Bi2Se3.

## Topological Insulators

- Author : M. Zahid Hasan,Su-Yang Xu,David Hsieh,L. Andrew Wray,Yuqi Xia
- Publisher :Unknown
- Release Date :2013-11-23
- Total pages :352
- ISBN : 9780128086872

**Summary :** Topological Surface States (TSS) represent new types of two dimensional electron systems with novel and unprecedented properties distinct from any quantum Hall-like or spin-Hall effects. Their topological order can be realized at room temperatures without magnetic fields and they can be turned into magnets, exotic superconductors or Kondo insulators leading to worldwide interest and activity in the topic. We review the basic concepts defining such topological matter and the key experimental probe that revealed the topological order in the bulk of these spin-orbit interaction dominated insulators. This review focuses on the key results that demonstrated the fundamental topological properties such as spin-momentum locking, non-trivial Berrys phases, mirror Chern number, absence of backscattering, protection by time-reversal and other discrete (mirror) symmetries and their remarkable persistence up to the room temperature elaborating on results first discussed by M.Z. Hasan and C.L. Kane in the Rev. of Mod. Phys., 82, 3045 (2010). Additionally, key results on broken symmetry phases such as quantum magnetism and uperconductivity induced in topological materials are briefly discussed.

## Topological Insulators

- Author : Ke He,Xucun Ma,Xi Chen,Qi-Kun Xue
- Publisher :Unknown
- Release Date :2013-11-23
- Total pages :352
- ISBN : 9780128086902

**Summary :** Material is a key to the experimental observation of novel quantum phenomena predicted in topological insulators. In this chapter, we review the recent theoretic and experimental efforts devoted to improving the existing topological insulator materials and exploring new topological insulators. The emphasis is on growth and engineering of the properties of topological insulator thin films by molecular beam epitaxy for realization of various quantum effects.

## Topological Insulators

- Author : Joel E. Moore
- Publisher :Unknown
- Release Date :2013-11-23
- Total pages :352
- ISBN : 9780128086834

**Summary :** 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

- Author : C. Brüne,H. Buhmann,L.W. Molenkamp
- Publisher :Unknown
- Release Date :2013-11-23
- Total pages :352
- ISBN : 9780128086865

**Summary :** This chapter will focus on the experimental properties of the quantum spin Hall effect in HgTe quantum well structures. HgTe quantum wells above a critical thickness are 2-dimensional topological insulators. The most prominent signature of the non-trivial topology in these systems is the occurrence of the quantum spin Hall effect when the Fermi energy is located inside the bulk band gap. We will present the main experimental results we obtained for transport in the quantum spin Hall regime and discuss how they confirm the prediction of the quantum spin Hall effect as a helical edge state system consisting of two counterpropagating oppositely spin polarized edge states.

## Berry Phases in Electronic Structure Theory

- Author : David Vanderbilt
- Publisher :Unknown
- Release Date :2018-10-31
- Total pages :421
- ISBN : 9781107157651

**Summary :** An introduction to the role of Berry phases in our modern understanding of the physics of electrons in solids.