This book covers basic and advanced aspects in the field of Topological Matter. The chapters are based on the lectures presented during the Topological Matter School 2017. It provides graduate level content introducing the basic concepts of the field, including an introductory session on group theory and topological classification of matter. Different topological phases such as Weyls semi-metals, Majoranas fermions and topological superconductivity are also covered. A review chapter on the major experimental achievements in the field is also provided. The book is suitable not only for master, graduate and young postdoctoral researchers, but also to senior scientists who want to acquaint themselves with the subject.

A geometric figure has chirality, or handedness, if its mirror image cannot be brought to coincide with itself. The concept of chirality was instrumental in establishing the tetrahedral valences of the carbon atom, and has continued to play a key role in chemistry and molecular biology ever since.The fact that living organisms use only one of two mirror isomers of such molecules as amino acids and sugars, that is, the question of the origin of homochirality of the molecular basis of life, remains an unsolved problem of the same dignity as the origin of dark matter and dark energy.The increasing importance of chirality and topology in condensed matter physics and chemistry, and the production of new states of matter in heavy-ion collisions, have brought the concept of chirality into physics and cosmology in a tangible way while at the same time expanded the physics/chemistry interface. The book is the first to address all aspects of chirality in a single volume.

Since the initial predictions for the existence of Weyl fermions in condensed matter, many different experimental techniques have confirmed the existence of Weyl semimetals. Among these techniques, optical responses have shown a variety of effects associated with the existence of Weyl fermions. In chiral crystals, we find a new type of fermions protected by crystal symmetries — the chiral multifold fermions — that can be understood as a higher-spin generalization of Weyl fermions. This work provides a complete description of all chiral multifold fermions, studying their topological properties and the k·p models describing them. We compute the optical conductivity of all chiral multifold fermions and establish their optical selection rules. We find that the activation frequencies are different for each type of multifold fermion, thus constituting an experimental fingerprint for each type of multifold fermion. Building on the theoretical results obtained in the first part of our analysis, we study two chiral multifold semimetals: RhSi and CoSi. We analyze the experimental results with k·p and tight-binding models based on the crystal symmetries of the material. We trace back the features observed in the experimental optical conductivity to the existence of multifold fermions near the Fermi level and estimate the chemical potential and the scattering lifetime in both materials. Finally, we provide an overview of second-order optical responses and study the second-harmonic generation of RhSi. We find a sizeable second-harmonic response in the low-energy regime associated with optical transitions between topological bands. However, this regime is extremely challenging to access with the current experimental techniques. We conclude by providing an overview of the main results, highlighting potential avenues to further research on chiral multifold semimetals and the future of optical responses as experimental probes to characterize topological phases.

"Quantum field theory is the mathematical and conceptual framework that describes the physics of the very small, including subatomic particles and quasiparticles. It is used to address a range of problems across subfields, from high-energy physics and gravitation to statistical physics and condensed matter physics. Despite the breadth of its applications, however, the teaching of quantum field theory has historically been strongly oriented toward high-energy physics students, while others-particularly in condensed matter and statistical physics-are typically taught in a separate course, or take an alternate sequence in many-body and statistical physics. Author Eduardo Fradkin strongly believes that this separation is both artificial and detrimental to all groups' understanding of quantum field theory. This textbook, developed from a graduate course Fradkin has taught for decades at the University of Illinois, offers a new, "multicultural" approach to the subject that seeks to remedy this fragmentation. It covers both basic techniques and topics at the frontiers of current research, and integrates modern concepts and examples from high-energy, statistical, and condensed-matter physics alike. Extensive problem sets further illustrate applications across a range of subfields. The book will be suitable for students across physical subdisciplines who have mastered graduate-level quantum mechanics, and will be a useful reference for researchers"--

What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid-state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture and emphasizing two major new paradigms in condensed matter physics – quantum topology and quantum information – this book is ideal for graduate students and researchers entering this field, as it allows for the fruitful transfer of ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and unveils the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the toric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Topological quantum computation is also presented using a broad perspective, which includes elements of classical and quantum information theory, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and key ideas underlying quantum computation with anyons. This new edition has been updated throughout, with exciting new discussions on crystalline topological phases, including higher-order topological insulators; gapless topological phases, including Weyl semimetals; periodically-driven topological insulators; and a discussion of axion electrodynamics in topological materials. Key Features: · Provides an accessible introduction to this exciting, cross-disciplinary area of research. · Fully updated throughout with new content on the latest result from the field. · Authored by an authority on the subject. Tudor Stanescu is a professor of Condensed Matter Theory at West Virginia University, USA. He received a B.S. in Physics from the University of Bucharest, Romania, in 1994 and a Ph.D. in Theoretical Physics from the University of Illinois at Urbana Champaign in 2002. He was a Postdoctoral Fellow at Rutgers University and at the University of Maryland from 2003 to 2009. He joined the Department of Physics and Astronomy at West Virginia University in Fall 2009. Prof. Stanescu’s research interests encompass a variety of topics in theoretical condensed matter physics including topological insulators and superconductors, topological quantum computation, ultra-cold atom systems in optical lattices, and strongly correlated materials, such as, for example, cuprate high-temperature superconductors. His research uses a combination of analytical and numerical tools and focuses on understanding the emergence of exotic states of matter in solid state and cold atom structures, for example, topological superconducting phases that host Majorana zero modes, and on investigating the possibilities of exploiting these states as physical platforms for quantum computation.

A sound understanding of magnetism, transport theory, spin relaxation mechanisms, and magnetization dynamics is necessary to engage in spintronics research. In this primer, special effort has been made to give straightforward explanations for these advanced concepts. This book will be a valuable resource for graduate students in spintronics and related fields. Concepts of magnetism such as exchange interaction, spin-orbit coupling, spin canting, and magnetic anisotropy are introduced. Spin-dependent transport is described using both thermodynamics and Boltzmann’s equation, including Berry curvature corrections. Spin relaxation phenomenology is accounted for with master equations for quantum spin systems coupled to a bath. Magnetic resonance principles are applied to describe spin waves in ferromagnets, cavity-mode coupling in antiferromagnets, and coherence phenomena relevant to spin qubits applications. Key Features: • A pedagogical approach to foundational concepts in spintronics with simple models that can be calculated to enhance understanding. • Nineteen chapters, each beginning with a historical perspective and ending with an outlook on current research. • 1200 references, ranging from landmark papers to frontline publications. Jean-Philippe Ansermet is Professor Emeritus at École Polytechnique Fédérale de Lausanne (EPFL), where he pioneered experiments on giant magnetoresistance, current-induced magnetization switching, heat-driven spin torque, and nuclear magnetic resonance. He taught mechanics, thermodynamics, and spin dynamics for more than twenty years. A fellow of the American Physical Society and recipient of the 2022 Credit Suisse Teaching Award, he was an executive board member of the European Physical Society, president of the Swiss Physical Society, and teaching director at EPFL. He has authored or co-authored textbooks on mechanics and thermodynamics and published more than two hundred articles.

Multi-author volume on the history and philosophy of physics.