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Topological insulators. --- Insulators, Topological --- Electric insulators and insulation --- Electronic apparatus and appliances --- Materials

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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.

Atomic Physics --- Physics --- Physical Sciences & Mathematics --- Mathematical physics. --- Magnetism. --- Solid State Physics. --- Mathematical Methods in Physics. --- Magnetism, Magnetic Materials. --- Semiconductors. --- Physical mathematics --- Mathematical physics --- Electricity --- Magnetics --- Mathematics --- Topological insulators. --- Topological manifolds. --- Solid state physics. --- Physics. --- Magnetic materials. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Solids --- Crystalline semiconductors --- Semi-conductors --- Semiconducting materials --- Semiconductor devices --- Crystals --- Electrical engineering --- Electronics --- Solid state electronics --- Materials

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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. .

Electric insulators and insulation. --- Dirac equation. --- Condensed matter. --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Bushings --- Insulation (Electric) --- Physics. --- Solid state physics. --- Semiconductors. --- Optical materials. --- Electronic materials. --- Solid State Physics. --- Optical and Electronic Materials. --- Differential equations, Partial --- Quantum field theory --- Wave equation --- Electric resistance --- Insulating materials --- Dielectrics --- Liquids --- Matter --- Solids --- Optics --- Materials --- Topological insulators. --- Electronic materials --- Physics --- Crystalline semiconductors --- Semi-conductors --- Semiconducting materials --- Semiconductor devices --- Crystals --- Electrical engineering --- Electronics --- Solid state electronics

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This book provides a model description for the electromagnetic response of topological nodal semimetals and summarizes recent experimental findings in these systems. Specifically, it discusses various types of topological semimetals – Dirac, Weyl, nodal-line, triple-point, and multifold semimetals – and provides description for the characteristic features of the linear electrodynamic response for all these types of materials. Topological semimetals possess peculiar bulk electronic band structure, which leads to unusual electrodynamic response. For example, the low-energy inter-band optical conductivity of nodal semimetals is supposed to demonstrate power-law frequency dependence and the intra- and inter-band contributions to the conductivity are often mixed. Further, the magneto-optical response is also unusual, because of the non-equidistant spacing between the Landau levels. Finally, in semimetals with chiral electronic bands, e.g. in Weyl semimetals, the simultaneous application of parallel magnetic and electric fields leads to the chiral anomaly, i.e. to a misbalance between the electrons with diffident chiralities. This misbalance affects the electrodynamics properties of the material and can be detected optically. All these points are addressed here in detail. The book is written for a wide audience of physicists, working in the field of topological condensed matter physics. It gives a pedagogical introduction enabling graduate students and non-experts to familiarize themselves with the subject.

Semimetals. --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Metalloids --- Metals --- Topological insulators. --- Metals. --- Condensed matter. --- Optical spectroscopy. --- Solid state chemistry. --- Topological Material. --- Metals and Alloys. --- Condensed Matter Physics. --- Optical Spectroscopy. --- Solid-State Chemistry. --- Chemistry, Solid state --- Chemistry, Physical and theoretical --- Spectroscopy, Optical --- Visible spectroscopy --- Spectrum analysis --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Metallic elements --- Chemical elements --- Ores --- Metallurgy --- Insulators, Topological --- Electric insulators and insulation --- Electronic apparatus and appliances --- Materials