Superconductivity in crystals with spin-orbit coupling

The electron Bloch states in crystals with spin-orbit coupling do not always transform under symmetry operations in the same way as the pure spin-1/2 states. This has profound consequences for the gap symmetry and nodal structure of superconductors. Based on the generalization of the Ueda-Rice prescription for the Bloch bases in twofold degenerate bands, we develop the general symmetry classification of multi-band superconducting pairing in non-magnetic centrosymmetric crystals. For the intraband pairing, we identify four exceptional cases in which the triplet gap function does not transform under the point group operations as a pseudovector, with a significant impact on the nodal structure. For the interband pairing, we show that the conventional (s-wave) gap functions can have such unconventional features as triplet components and odd parity. The d-wave interband pairing can also be odd in momentum and have a triplet component.