Two key ideas concerning unconventional superconductors are the following.
1. s-wave and p-wave pairing (in momentum space) are associated with spin singlet and spin triplet pairing, respectively. This can be shown with minimal assumptions (no spin-orbit coupling and spatial inversion symmetry).
2. If superconductivity is seen in proximity to an ordered phase (e.g. ferromagnetism or antiferromagnetism) with a quantum critical point (QCP) then the pairing can be "mediated" by low energy fluctuations (e.g. magnons) associated with the ordering.
3. Non-fermi liquid behaviour may be seen in the quantum critical region about the QCP.
However, an interesting paper shows that neither of the above is necessarily true.
Superconductivity from Emerging Magnetic Moments
Shintaro Hoshino and Philipp Werner
They find spin triplet superconductivity with s-wave symmetry. This arises because there is more than one orbital per site and due to the Hund's rule coupling spin triplets can form on a single site.
They also find the pairing is strongest near the "spin freezing crossover" which is associated with the "Hund's metal", i.e. the bad metal arising from the Hund's rule interaction, and has certain "non-Fermi liquid" properties.
The results are summarised in the phase diagrams below, which has a striking similarity to various experimental phase diagrams that are usually interpreted in terms of 2. above.
However, all the theory is DMFT and so there are no long wavelength fluctuations.