For the past almost fifty years, scientists have been trying to explain the phenomenon of superconductivity. The mechanism is the key ingredient of microscopic theory, which was developed by Bardeen, Cooper, and Schrieffer in 1957. The theory also introduced the basic concepts of pairing, coherence length, energy gap, and so on. Since then, microscopic theory has undergone an intensive development. This book provides a very detailed theoretical treatment of the key mechanisms of superconductivity, including the current state of the art (phonons, magnons, plasmons). In addition, the book contains descriptions of the properties of the key superconducting compounds that are of the most interest for science and applications. For many years, there has been a search for new materials with higher values of the main parameters, such as the critical temperature and critical current. At present, the possibility of observing superconductivity at room temperature has become perfectly realistic. That is why the book is especially concerned with high-Tc systems such as high-Tc oxides, hydrides with record values for critical temperature under high pressure, nanoclusters, and so on. A number of interesting novel superconducting systems have been discovered recently, including topological materials, interface systems, and intercalated graphene. The book contains rigorous derivations based on statistical mechanics and many-body theory. The book also provides qualitative explanations of the main concepts and results. This makes the book accessible and interesting for a broad audience.
Some Characterizations of the Distribution of the Condition Number of a Complex Gaussian Matrix
