Pair-breaking in superconductors with strong spin-orbit coupling

We present a general theory for the pair-breaking effect of an arbitrary external perturbation in a multiband superconductor with strong spin-orbit coupling. Our central result is that the pair-breaking can be quantified by a single measure which we dub the "field-fitness function", which incorporates the interplay of the normal-state spin-orbital texture with both the pairing potential and the perturbation. This parameter controls the suppression of the critical temperature and, for the case of an external magnetic field, the magnitude of the Knight shift in the superconducting state. For even-parity superconductors we find that the field-fitness function for an external magnetic field is one, implying maximal pair-breaking consistent with Anderson's theorem. For odd-parity superconductors, in contrast, the field-fitness function reveals a more complicated interplay which can yield counter-intuitive behaviour. We apply our method to the topical case of p-wave pairing in the effective j = 3/2 electronic states of the Luttinger-Kohn model.