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This book surveys the science at a semipopular, Scientific American-level. It is even-handed with regard to competing directions of research and philosophical positions. It is hard to get even two people to agree on anything, yet a million billion water molecules can suddenly and abruptly coordinate to lock themselves into an ice crystal or liberate one another to billow outwards as steam. The marvelous self-organizing capacity of matter is one of the central and deepest puzzles of physics, with implications for all the natural sciences. Physicists in the past century have found a remarkable diversity of phases of matter-and equally remarkable commonalities within that diversity. The pace of discovery has, if anything, only quickened in recent years with the appreciation of quantum phases of matter and so-called topological order. The study of seemingly humdrum materials has made contact with the more exotic realm of quantum gravity, as theorists realize that the spacetime continuum may itself be a phase of some deeper and still unknown constituents. These developments flesh out the sometimes vague concept of the emergence-how exactly it is that complexity begets simplicity.

Solid state physics --- Geophysics --- zwaartekracht --- fysica --- Condensed matter. --- Quantum gravity. --- Topological insulators.

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This book focuses on nanoscale electronic phase separation in a wide class of different materials, especially in strongly correlated electron systems. It features an extensive review of the field of inhomogeneous spin and charge states in condensed matter physics while delivering a topical and timely discussion of a wide range of recent advances in electronic phase separation. It describes the formation of different types of nanoscale ferromagnetic metallic droplets in antiferromagnetically ordered, charge-ordered, or orbitally-ordered insulating matrices, as well as the colossal magnetoresistance effect and tunneling electron transport in the nonmetallic phase-separated state of complex magnetic oxides. It also discusses compounds with spin-state transitions, inhomogeneously phase-separated states in strongly correlated multiband systems, and the electron polaron effect, paying special attention to systems with imperfect Fermi surface-nesting such as chromium alloys, iron-based pnictides, and AA-stacked graphene bilayers. The authors investigate also the formation of order parameter clusters and insulator-superconductor transition in different superconducting systems including bismuth oxides, two-dimensional films in the presence of strong disorder, as well as inhomogeneous Fermi-Bose mixtures in Aharonov-Bohm rings with a superconducting bridge in a topologically nontrivial state. This book is a valuable resource for researchers involved in theoretical and experimental studies of strongly correlated materials, such as magnetic semiconductors, Fermi-Bose mixtures, and twisted bilayer graphene.

Condensed matter. --- Magnetism. --- Low temperatures. --- Topological insulators. --- Strongly Correlated Systems. --- Low Temperature Physics. --- Two-dimensional Materials. --- Topological Material.

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Topological insulators. --- Kondo effect. --- Fermions. --- Fermi-Dirac particles --- Particles (Nuclear physics) --- Quantum statistics --- Interacting boson-fermion models --- Leptons (Nuclear physics) --- Electric resistance --- Magnetic materials --- Solids --- Insulators, Topological --- Electric insulators and insulation --- Electronic apparatus and appliances --- Electric properties --- Materials

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Condensed matter. --- Quantum gravity. --- Topological insulators. --- Insulators, Topological --- Electric insulators and insulation --- Electronic apparatus and appliances --- Gravity, Quantum --- General relativity (Physics) --- Gravitation --- Quantum theory --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- 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