Unconventional superconductivity mediated by the "Higgs" amplitude mode in itinerant ferromagnets

Over 20 years ago, Blagoev et. al. [Phys. Rev. Lett. 82, 133 (1999)] predicted an s-wave pairing instability in a ferromagnetic Fermi liquid (FFL) as a consequence of spin fluctuations. Shortly after, it was discovered that, when magnetic interactions in the ferromagnetic superconductor UGe2 dominate, quasiparticles with parallel spin form pairs in odd-parity orbitals; i.e., a form of spin-triplet p-wave superconductivity emerges, in contrast to Blagoev et. al.'s prediction. In this work, we return to this issue by introducing the effects of a gapped amplitude (or "Higgs") mode on the vertex corrections and subsequent form of Cooper pairing. As the Higgs mode only propagates in the presence of a finite spin current, such an amplitude mode results in strong momentum-dependence in the many-body vertex. This results in the emergence of an unconventional form of superconductivity mediated by unconventional low-energy modes in a weak itinerant ferromagnet.