Introduction.- Review of Symmetry and Representations in Band Theory.- Review of Symmetry and Representations in Band Theory.- Classifications of Superconducting Nodes.- High-throughput Investigation.

This book develops a symmetry-based approach to superconductors, which enables us to efficiently diagnose topological and nodal superconductivity. Superconductivity has fascinated physicists since its first discovery. In particular, unconventional superconductivity, which arises from unusual attractive interactions between electrons, has been intensively studied for the last few decades. More recently, it turns out that topological nature of superconductivity is closely related to how electrons pair up. After reviewing the basic concepts of the symmetry-based analysis of band topology, the first part of this book discusses a generalization of symmetry-based indicators—an efficient way to diagnose topological insulating phases without full information on wave functions—to superconducting phases. The second part of this book develops a novel scheme to extensively classify superconducting nodes—geometry of gapless regions in the Bogoliubov quasiparticle spectrum—based on band topology.Finally, combining these two parts, this book proposes a systematic scheme to predict topological and nodal properties of the superconducting phase by considering various possible pairing symmetries.