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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.

Energy-band theory of solids. --- Superconductivity. --- Solid state physics --- Superconductors --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Physics --- Solids --- Electric conductivity --- Critical currents --- Superfluidity --- Band theory of solids --- Conduction band --- Crystallography, Mathematical --- Electrons --- Exciton theory --- Molecules --- Quantum theory --- Wave mechanics --- Mathematics. --- Materials

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In this book the author presents two important findings revealed by high-precision magnetic penetration depth measurements in iron-based superconductors which exhibit high-transition temperature superconductivity up to 55 K: one is the fact that the superconducting gap structure in iron-based superconductors depends on a detailed electronic structure of individual materials, and the other is the first strong evidence for the presence of a quantum critical point (QCP) beneath the superconducting dome of iron-based superconductors. The magnetic penetration depth is a powerful probe to elucidate the superconducting gap structure which is intimately related to the pairing mechanism of superconductivity. The author discusses the possible gap structure of individual iron-based superconductors by comparing the gap structure obtained from the penetration depth measurements with theoretical predictions, indicating that the non-universal superconducting gap structure in iron-pnictides can be interpreted in the framework of A1g symmetry. This result imposes a strong constraint on the pairing mechanism of iron-based superconductors. The author also shows clear evidence for the quantum criticality inside the superconducting dome from the absolute zero-temperature penetration depth measurements as a function of chemical composition. A sharp peak of the penetration depth at a certain composition demonstrates pronounced quantum fluctuations associated with the QCP, which separates two distinct superconducting phases. This gives the first convincing signature of a second-order quantum phase transition deep inside the superconducting dome, which may address a key question on the general phase diagram of unconventional superconductivity in the vicinity of a QCP.

Superconductivity. --- Superconductors -- Industrial applications. --- Superconductors -- Research -- History. --- Superconductivity --- Iron-based superconductors --- High temperature superconductors --- Physics --- Physical Sciences & Mathematics --- Electricity & Magnetism --- High temperature superconductors. --- Physics. --- Quantum physics. --- Superconductors. --- Magnetism. --- Magnetic materials. --- Strongly Correlated Systems, Superconductivity. --- Quantum Physics. --- Magnetism, Magnetic Materials. --- Electric conductivity --- Critical currents --- Superfluidity --- Materials at low temperatures --- Superconductors --- Quantum theory. --- Mathematical physics --- Electricity --- Magnetics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Materials --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics

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This book presents an investigation of the anomalous and topological Hall effects in some itinerant ferromagnets and helimagnets by measurements of Hall effects driven by electrical or heat current. New clarifications are provided for spin-dependent Hall effects induced by the Berry phase, skew scattering, and scalar spin chirality. The author reveals the scattering-free nature of the Berry-phase-induced anomalous Hall current by conducting the first comparative study of electrical and thermal Hall effects. The impurity-element dependence of the anomalous Hall effect caused by skew scattering is systematically investigated in the low-resistivity region for Fe. Two new examples showing a topological Hall effect are found in helimagnets, in which nonzero scalar spin chirality arises from the modulation of spin structure through Dzyaloshinsky–Moriya (DM) interaction. Such a DM-interaction-mediated topological Hall effect is a new type of topological Hall effect. Also the temperature dependence of topological Hall terms in the thermal Hall effect and Nernst–Ettingshausen effect is found to be totally different from that in the electrical Hall effect. These results will be useful for applications of spin current to devices with low power consumption.

Hall effect. --- Magnetism, Band theory of. --- Salt. --- Hall effect --- Magnetism, Band theory of --- Physics --- Physical Sciences & Mathematics --- Electricity & Magnetism --- Magnetism. --- Physics. --- Superconductivity. --- Superconductors. --- Magnetic materials. --- Electronic circuits. --- Strongly Correlated Systems, Superconductivity. --- Magnetism, Magnetic Materials. --- Electronic Circuits and Devices. --- Mathematical physics --- Electricity --- Magnetics --- Electric currents --- Galvanomagnetic effects --- Gyrators --- Electron-tube circuits --- Electric circuits --- Electron tubes --- Electronics --- Materials --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Solid state electronics --- Electric conductivity --- Critical currents --- Superfluidity

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This thesis describes a novel and robust way of deriving a Hamiltonian of the interacting boson model based on microscopic nuclear energy density functional theory. Based on the fact that the multi-nucleon induced surface deformation of finite nucleus can be simulated by effective boson degrees of freedom, intrinsic properties of the nucleon system, obtained from self-consistent mean-field method with a microscopic energy density functional, are mapped onto the boson analog. Thereby, the excitation spectra and the transition rates for the relevant collective states having good symmetry quantum numbers are calculated by the subsequent diagonalization of the mapped boson Hamiltonian. Because the density functional approach gives an accurate global description of nuclear bulk properties, the interacting boson model is derived for various situations of nuclear shape phenomena, including those of the exotic nuclei investigated at rare-isotope beam facilities around the world. This work provides, for the first time, crucial pieces of information about how the interacting boson model is justified and derived from nucleon degrees of freedom in a comprehensive manner.

Nuclear physics. --- Nuclear shell theory. --- Nuclear structure. --- Interacting boson models --- Density functionals --- Physics --- Physical Sciences & Mathematics --- Electricity & Magnetism --- Bosons. --- Physics. --- Magnetism. --- Natural philosophy --- Philosophy, Natural --- Bose-Einstein particles --- Mathematical physics. --- Superconductivity. --- Superconductors. --- Magnetic materials. --- Strongly Correlated Systems, Superconductivity. --- Magnetism, Magnetic Materials. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Applications in the Physical Sciences. --- Mathematical physics --- Electricity --- Magnetics --- Physical sciences --- Dynamics --- Particles (Nuclear physics) --- Interacting boson-fermion models --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Electric conductivity --- Critical currents --- Superfluidity --- Physical mathematics --- Materials --- Mathematics

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Thermodynamics is a well-established discipline of physics for properties of matter in thermal equilibrium with the surroundings. Applying to crystals, however, the laws encounter undefined properties of crystal lattice, which therefore need to be determined for a clear and well-defined description of crystalline states. Thermodynamics of Crystalline States explores the roles played by order variables and dynamic lattices in crystals in a wholly new way. The book begins by clarifying basic concepts for stable crystals. Next, binary phase transitions are discussed to study collective motion of order variables, as described mostly as classical phenomena. New to this edition is the examination of magnetic crystals, where magnetic symmetry is essential for magnetic phase transitions. The multi-electron system is also discussed  theoretically, as a quantum-mechanical example, for superconductivity in metallic crystals. Throughout the book, the role played by the lattice is emphasized and studied in-depth. Thermodynamics of Crystalline States is an introductory treatise and textbook on mesoscopic phenomena in solid states, constituting a basic subject in condensed matter physics. While this book serves as a guide for advanced students in physics and material science, it can also be useful as a reference for all professionals in related fields. Minoru Fujimoto is author of Physics of Classical Electromagnetism (Springer, 2007) and The Physics of Structural Phase Transitions (Springer, 2005).

Crystal lattices. --- Thermodynamics. --- Crystal lattices --- Crystals --- Chemical & Materials Engineering --- Physics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Thermodynamics --- Materials Science --- Thermal properties --- Thermal properties. --- Lattices --- Physics. --- Physical chemistry. --- Solid state physics. --- Crystallography. --- Superconductivity. --- Superconductors. --- Solid State Physics. --- Physical Chemistry. --- Strongly Correlated Systems, Superconductivity. --- Crystallography, Mathematical --- Lattice theory --- Twinning (Crystallography) --- Chemistry, Physical organic. --- Crystallography and Scattering Methods. --- Leptology --- Physical sciences --- Mineralogy --- Chemistry, Physical organic --- Chemistry, Organic --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Heat --- Heat-engines --- Quantum theory --- Solids --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Electric conductivity --- Critical currents --- Superfluidity --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry --- Materials