High-Throughput Investigation

So far, we have developed theoretical frameworks to diagnose topological and nodal superconductivity based on band topology. As mentioned in Chap.  1 , investigating nodal and topological superconductivity of realistic materials is one of the important steps to elucidate the mechanisms of superconductivity in unconventional superconductors. Unfortunately, experimentally confirmed nodal and topological superconductors are significantly scarce compared to topological insulators and semimetals. Given the success of comprehensive investigations of topological insulators and semimetals based on symmetry-indicator theory and topological quantum chemistry, one might think that the establishment of such a database for superconductors would significantly boost the search for new topological superconductor candidates. However, because pairing symmetries of actual materials are usually unknown; consequently, this attempt is quite challenging. In this chapter, we avoid dealing with this difficulty and take an alternative approach: We apply the theories developed in Chaps. 3 and 4 to materials by assuming various possible pairing symmetries and build a database summarizing the topological and nodal superconducting nature of the materials for the assumed pairings.