Kohn-Luttinger Superconductivity of Weyl Fermi Arcs in PtBi$_2$

Recent experimental observations in the noncentrosymmetric Weyl semimetal PtBi$_2$ indicate unconventional superconductivity hosted by topological surface states -- Weyl Fermi arcs -- with a node at the center of each arc. Focusing on these Fermi arcs, we calculate the electronically mediated pairing interaction using a Kohn-Luttinger approach and find that, in a large region of the phase diagram, the leading superconducting instability has an $i$-wave symmetry featuring precisely such an intra-arc node. We study the dependence of the leading superconducting instabilities on electronic interaction parameters and chemical potential and show that the $i$-wave state is robust to changes in the model parameters. Our results provide a possible mechanism for the observation of topological $i$-wave superconductivity on the surface of PtBi$_2$ and may have implications for the broader landscape of superconducting instabilities arising from repulsive interactions on the surfaces of Weyl semimetals.