Recent experiments on non-magnetic Weyl semimetals have seen separate bulk and surface superconductivity in Weyl semimetals, which raises the question of whether the surface Fermi arcs can support intrinsic superconductivity while the bulk stays in the normal state. A theoretical answer to this question is hindered by the absence of a well-defined surface Hamiltonian since the Fermi arcs merge with the bulk states at their endpoints. Using an alternate, Green's functions-based approach on a phenomenological model that can yield arbitrary Fermi arcs, we show -- within mean-field theory -- that the surface can support a standard Cooper instability while the bulk remains disordered. Although the surface has lower dimensionality, a higher density of states compared to the bulk allows it to have a higher mean-field superconducting transition temperature.

11 pages, 4 figures