Geometry and topology have been a fascination in physics since the start of the 20th century. A leading example is Einstein's geometrical theory of gravity. At the beginning of the 1970s, topological ideas entered areas of condensed matter physics. These advances were driven by new seminal ideas resolving a serious contradiction between experiment and the standard interpretation of a rigorous mathematical theorem which led to the study of new exotic topological phases of matter. Topological defect driven phase transitions in thin, two dimensional films of superfluids, superconductors and crystals have provided great insight into the mechanism governing these topological phases present in those physical systems. Moreover, many of these topological properties remain 'protected' against disorder and topological distortion perturbations. An example of possible applications of such robustness to perturbations is in the search for encoding information in quantum computers, potentially providing the platform for fault-tolerant quantum computations.In the past four decades, the discovery of topological phases engendered great interest in condensed matter physics. It also attracted the attention of researchers working on quantum information, quantum materials and simulations, high energy physics and string theory. This unique volume contains articles written by some of the most prominent names in the field, including Nobel Laureate John Michael Kosterlitz and Professor Jorge V José. They originate from talks and discussions by leading experts at a recent workshop. They review previous works as well as addressing contemporary developments in the most pressing and important issues on various aspects of topological phases and topological phase transitions.

The fractional quantum Hall effect has been one of the most active areas of research in quantum condensed matter physics for nearly four decades, serving as a paradigm for unexpected and exotic emergent behavior arising from interactions. This book, featuring a collection of articles written by experts and a Foreword by Klaus von Klitzing, the discoverer of quantum Hall effect and winner of 1985 Nobel Prize in physics, aims to provide a coherent account of the exciting new developments and the current status of the field.

Topological insulator is one of the hottest research topics in solid state physics. This is the first book to describe the vibrational spectroscopies and electrical transport of topological insulator Bi2Se3, one of the most exciting areas of research in condensed matter physics. In particular, attempts have been made to summarize and develop the various theories and new experimental techniques developed over years from the studies of Raman scattering, infrared spectroscopy and electrical transport of topological insulator Bi2Se3. It is intended for material and physics researchers and graduate students doing research in the field of optical and electrical properties of topological insulators, providing them the physical understanding and mathematical tools needed to engage research in this quickly growing field. Some key topics in the emerging field of topological insulators are introduced.

The two experimental studies reported in this thesis contribute important new knowledge about phase transitions in two-dimensional complex plasmas: in one case a determination of the coupling parameter (ratio of mean potential to mean kinetic energy of the particles in an ensemble), and in the other a detailed characterization of the non-equilibrium recrystallization of a two-dimensional system. The latter results are used to establish the connection between structural order parameters and the kinetic energy, which in turn gives novel insights into the underlying physical processes determining the two-dimensional phase transition.

A unique and timely book providing an overview of both the methodologies and applications of computational materials design.

This book presents experimental studies on emergent transport and magneto-optical properties in three-dimensional topological insulators with two-dimensional Dirac fermions on their surfaces. Designing magnetic heterostructures utilizing a cutting-edge growth technique (molecular beam epitaxy) stabilizes and manifests new quantization phenomena, as confirmed by low-temperature electrical transport and time-domain terahertz magneto-optical measurements. Starting with a review of the theoretical background and recent experimental advances in topological insulators in terms of a novel magneto-electric coupling, the author subsequently explores their magnetic quantum properties and reveals topological phase transitions between quantum anomalous Hall insulator and trivial insulator phases; a new topological phase (the axion insulator); and a half-integer quantum Hall state associated with the quantum parity anomaly. Furthermore, the author shows how these quantum phases can be significantly stabilized via magnetic modulation doping and proximity coupling with a normal ferromagnetic insulator. These findings provide a basis for future technologies such as ultra-low energy consumption electronic devices and fault-tolerant topological quantum computers.

This thesis deals with topological orders from two different perspectives: from a condensed matter point of view, where topological orders are considered as breakthrough phases of matter; and from the emerging realm of quantum computation, where topological quantum codes are considered the most appealing platform against decoherence. The thesis reports remarkable studies from both sides. It thoroughly investigates a topological order called the double semion model, a counterpart of the Kitaev model but exhibiting richer quasiparticles as excitations. A new model for symmetry enriched topological order is constructed, which adds an onsite global symmetry to the double semion model. Using this topological phase, a new example of topological code is developed, the semion code, which is non-CSS, additive, non-Pauli and within the stabiliser formalism. Furthermore, the thesis analyses the Rashba spin-orbit coupling within topological insulators, turning the helical edge states into generic edges modes with potential application in spinstronics. New types of topological superconductors are proposed and the novel properties of the correspondingly created Majorana fermions are investigated. These Majorana fermions have inherent properties enabling braiding and the performance of logical gates as fundamental blocks for a universsal quantum computator.

Encyclopedia of Interfacial Chemistry: Surface Science and Electrochemistry, Seven Volume Set summarizes current, fundamental knowledge of interfacial chemistry, bringing readers the latest developments in the field. As the chemical and physical properties and processes at solid and liquid interfaces are the scientific basis of so many technologies which enhance our lives and create new opportunities, its important to highlight how these technologies enable the design and optimization of functional materials for heterogeneous and electro-catalysts in food production, pollution control, energy conversion and storage, medical applications requiring biocompatibility, drug delivery, and more. This book provides an interdisciplinary view that lies at the intersection of these fields. Presents fundamental knowledge of interfacial chemistry, surface science and electrochemistry and provides cutting-edge research from academics and practitioners across various fields and global regions

This book presents the findings of a major research program investigating structural design and controllable preparation of function-directed crystalline materials. The program was launched by the National Natural Science Foundation of China during the 11th Five-Year Plan period, which was started in October 2008 and concluded at the end of 2016. This book first summarizes the overall scientific objectives and the current state of the art of crystalline materials research in China and the international frontier. It also focuses on exploring the relationships between structures, compositions, and properties of crystalline materials and proposes new mechanisms and models for new materials exploration. In addition, it introduces a new functional-motif theory that can guide the development of crystalline materials with optical, electrical, and other composite functions and presents new research methods for the controlled synthesis and assembly of crystalline materials, and detection and characterization of functional motifs. Furthermore, practical applications for materials such as photoelectric conversion materials, nonlinear optical materials, laser and fluorescent crystal materials, and ferroelectric and microwave dielectric materials have been described. Given its scope, this book is of interest to researchers who work in crystalline materials. It also promotes the multidisciplinary collaboration among chemistry, materials science, and physics.

The work shows the fascination of topology- and geometry-governed properties of self-rolled micro- and nanoarchitectures. The author provides an in-depth representation of the advanced theoretical and numerical models for analyzing key effects, which underlie engineering of transport, superconducting and optical properties of micro- and nanoarchitectures.