Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries

Symmetry properties of Cooper pairs play a pivotal role in studies on topological superconductivity. Unconventional superconductors, whose pairing symmetries are different from conventional Bardeen-Cooper-Schrieffer superconductors, have been paid attention to as a platform of topological superconductivity. However, pairing symmetries of most superconductors are actually the conventional one and these superconductors are usually considered to be topologically trivial. In this work, combining the real-space and the momentum space approaches developed recently, we conduct classifications of time-reversal symmetric topological superconductors with conventional pairing symmetries. Remarkably, we find topological superconducting phases in 199 out of 230 space groups. Our finding sheds light on superconductors with conventional pairing symmetries as candidates for topological superconductors.