Unconventional Superconductivity arising from Multipolar Kondo Interactions

I am still not satisfied by the author’s explanation of the “mixing” of order parameters in different irreps. I undestand that their Hamiltonian does not break symmetry. However, if converted to LG notation, their Hamiltonian states that OP1 couples to the *spatial gradient* of OP2 with the appropriate symmetry (and vice versa), since the scattering vertex is q dependent and symmetry breaking. This is not the same as mixing irreps, which would be q-independent. It does not mean that once OP1 exists, OP2 also exists, which is the common meaning of mixing/coexisting OPs. I assume this coupling, which always exists in a LG expansion, has a particularly large coefficient due to the unusual Kondo interaction, and so this spatial gradient is likely to be substantially present? Their language here is misleading and should be corrected.

I am also concerned by their derivation of this q-dependent interaction vertex. Typically, if I write down a pairing interaction with f(q = k-k’) = cos qx - cos qy, then I separate it into even/odd parity components with f(k-k’) +/- f(k+k’) and then separate these to write f(k) f(k’), where then the d-wave symmetry of f(q) is actually split between the two superconducting order parameters, as opposed to keeping it with the interaction vertex, as they do here. Now, given the symmetry of the Gamma’s involved, they may be correct to do what they have done, however, it is at all not obvious. Given that what they are doing is so unusual, they must explain why their choice is the correct one, in detail, particularly why the momentum dependence is being kept with the vertex rather than going with the superconducting order parameter.

These are serious concerns, and I cannot support publication until they are addressed.

The authors answer all the comments properly and the revised manuscript is easier to follow. Thus, I believe the paper is now suitable for publication.