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Topological Phases of Matter are an exceptionally dynamic field of research: several of the most exciting recent experimental discoveries and conceptual advances in modern physics have originated in this field. These have generated new, topological, notions of order, interactions and excitations. This text provides an accessible, unified and comprehensive introduction to the phenomena surrounding topological matter, with detailed expositions of the underlying theoretical tools and conceptual framework, alongside accounts of the central experimental breakthroughs. Among the systems covered are topological insulators, magnets, semimetals, and superconductors. The emergence of new particles with remarkable properties such as fractional charge and statistics is discussed alongside possible applications such as fault-tolerant topological quantum computing. Suitable as a textbook for graduate or advanced undergraduate students, or as a reference for more experienced researchers, the book assumes little prior background, providing self-contained introductions to topics as varied as phase transitions, superconductivity, and localisation.

Condensed matter. --- Geometric quantum phases. --- Topological defects (Physics) --- Topology.

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The concept of topology has become commonplace in various scientific fields. This volume contains articles on experiments and theories in connection with topology, including fields such as materials science, superconductivity, charge density waves, superfluidity, optics, and field theory.

Topological defects (Physics) --- Topology --- Defects, Topological (Physics) --- Phase rule and equilibrium

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Ginzburg-Landau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to Ginzberg-Landau theory, both common and topological excitations are considered on the same footing (including their thermodynamics and dynamical phenomena). The role of the topological versus energetic considerations is made clear. Required mathematics (symmetry, including lattice translation, topology, and perturbative techniques) are introduced as needed. The results are illustrated using arguably the most fascinating class of such systems, high Tc superconductors subject to magnetic field. This book is an important reference for both researchers and graduate students working in condensed matter physics or can act as a textbook for those taking advanced courses on these topics.

Condensed matter. --- Phase transformations (Statistical physics) --- Topological defects (Physics) --- Superconductivity. --- Vortex-motion. --- Matière condensée --- Transitions de phases --- Loi des phases et équilibre --- Théorie de Ginzburg-Landau --- Tourbillons (mécanique des fluides) --- Condensed matter --- Superconductivity --- Vortex-motion --- Electric conductivity --- Critical currents --- Superfluidity --- Defects, Topological (Physics) --- Phase rule and equilibrium --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Statistical physics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Aerodynamics --- Eddies --- Fluid dynamics --- Hydrodynamics --- Rotational motion --- 538.9 --- 538.9 Physics of condensed matter (in liquid state and solid state) --- Physics of condensed matter (in liquid state and solid state) --- Matière condensée --- Loi des phases et équilibre --- Théorie de Ginzburg-Landau --- Tourbillons (mécanique des fluides)