Pairing of Anomalous Pseudospin

In non-centrosymmetric materials, the resultant generalized Rashba spin-orbit coupling leads to novel behavior of superconductivity, allowing, for example, critical fields exceeding the Pauli field for singlet-superconductors, singlet-triplet mixing, and symmetry-dictated finite momentum pairing states. In locally non-centrosymmetric materials, generalizations of this novel behavior appear even when inversion symmetry is present, provided the spin-orbit coupling is sufficiently strong. Here we further generalize this through the introduction of anomalous pseudospin, which reveals that spin-orbit coupling dominates in materials with inversion symmetry, even without inversion-related sectors in the crystal structure. We classify all TRIM on momentum planes that allow anomalous pseudospin and highlight the resultant superconducting properties for Fermi surfaces near these momentum planes. We show how the superconducting pairing of anomalous pseudospin allows for an unusual response to magnetic fields and gives rise to a novel manifestation of nodal excitations.