  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.
