Superconductivity in crystals with spin-orbit coupling

Abstract

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 ([Formula: see text]-wave) gap functions can have such unconventional features as triplet components and odd parity. The [Formula: see text]-wave interband pairing can also be odd in momentum and have a triplet component.