Topology Condensed

This book highlights a comprehensive introduction of graphene and graphene-based two-dimensional nanomaterials, covering topics from their atomic structures, electronic band structures, and fundamental properties to technological applications. The book provides fundamental physics knowledge covering quantum mechanics, the theory of relativity, solid-state physics, and topology geometry necessary to understand electronic band structure of graphene. Other topics including microscopy techniques and preparation methods of graphene are also presented. Adopting an easy-to-read style, the book is a valuable resource for researchers in physics, chemistry, materials science, and engineers who are interested in the field of graphene-based nanomaterials.

This book provides an accessible yet rigorous overview of current research in topology, making it an invaluable resource for mathematicians, physicists, and researchers in related fields.

This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics.

Impurities, disorder or amorphous systems – ill-condensed matter – are mostly considered inconveniences in the study of materials, which is otherwise heavily based on idealized perfect crystals. The Kondo effect and the scaling theory of localization are among the fundamental and early discoveries which revealed the novelty hidden in impure or disordered systems. Recent advances in condensed matter physics have emphasized the role of topology, spin-orbit coupling, and certain discrete symmetries such as time reversal in many physical phenomena. These have irreversibly transformed the essential ideas and purview of condensed matter physics, both in theoretical and experimental directions.