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Author: B. Andrei Bernevig Publisher: Princeton University Press ISBN: 1400846730 Category : Science Languages : en Pages : 264
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: B. Andrei Bernevig Publisher: Princeton University Press ISBN: 1400846730 Category : Science Languages : en Pages : 264
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: Gaurav Chaudhary (Ph. D.) Publisher: ISBN: Category : Languages : en Pages : 284
Book Description
This dissertation presents studies of topological superconductivity in Chern insulator systems. In particular, when a Chern insulator such as a quantum Hall or a quantum anomalous Hall system is proximity coupled to a trivial s-wave superconductor. While quantum anomalous Hall based system is investigated in detail in both one and two dimensions, the focus is solely on two dimensions in quantum Hall bases system. Both quantum Hall and quantum anomalous Hall break time reversal (T)-symmetry. Hence throughout this thesis, we focus on the T-symmetry broken topological superconductor systems, which fall in the class [double struck D] of the Altland-Zirnbauer classification. After a brief introduction to thesis in chapter 1 and review of topological superconductivity in chapter 2, in chapter 3, a realistic system motivated from the experimental observation of the quantum anomalous Hall effect is considered. The focus of this chapter is on one dimensional (1D) topological superconducting phase in thin ribbon geometries [Phys. Rev. B 97, 081102(R)]. It identifies the quantum anomalous Hall based system as highly controllable platform for Majorana zero modes, which can be potentially used as Majorana braiding device. In chapter 4, two dimensional (2D) topological superconducting phase in the quantum Hall based system is studied [arXiv:1903.12249]. Because of the inherent requirement of the external magnetic field to achieve quantum Hall physics, this system requires consideration of vortex lattice phase in the parent superconductor. It is shown that the topological superconducting phase is determined by the type of vortex lattice. Hence, making quantum Hall based system different than quantum anomalous Hall based system, giving much richer phase diagram. Experimental protocol to engineer and observe Majorana edge modes in this system is also discussed. In chapter 5, reentrant superconductivity under magnetic fields beyond semiclassical critical magnetic field is discussed. It is argued that recently discovered superconductivity in magic angle twisted bilayer graphene (MATBG) can be a promising ground to observe this phase. In chapter 6, recent transport experiments in quantum anomalous Hall/superconductor devices are discussed. The two main experiments on this system have contradictory results and there is widespread debate on possible explanations of the experimental observations, which can born out of chiral Majorana mode (i.e. topological) or disorder (i.e. trivial). The main arguments on both sides are summarized and some strategies to resolve the debate are proposed
Author: János K. Asbóth Publisher: Springer ISBN: 3319256076 Category : Science Languages : en Pages : 176
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: Gregory Tkachov Publisher: CRC Press ISBN: 9814613266 Category : Science Languages : en Pages : 180
Book Description
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 car
Author: Huixia Luo Publisher: John Wiley & Sons ISBN: 1119407338 Category : Technology & Engineering Languages : en Pages : 431
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: Michael I. Monastyrsky Publisher: Springer Science & Business Media ISBN: 3540312641 Category : Science Languages : en Pages : 263
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: Roderich Moessner Publisher: Cambridge University Press ISBN: 1107105536 Category : Mathematics Languages : en Pages : 393
Book Description
This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.
Author: Panagiotis Kotetes Publisher: Morgan & Claypool Publishers ISBN: 1681745178 Category : Science Languages : en Pages : 216
Book Description
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.
Author: Naoto Nagaosa Publisher: Elsevier Inc. Chapters ISBN: 0128086912 Category : Science Languages : en Pages : 39
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: B. Andrei Bernevig
Author: B. Andrei Bernevig
Author: Gaurav Chaudhary (Ph. D.)
Author: Doru Sticlet
Author: János K. Asbóth
Author: Gregory Tkachov
Author: Huixia Luo
Author: Michael I. Monastyrsky
Author: Roderich Moessner
Author: Panagiotis Kotetes
Author: Naoto Nagaosa