Phonon-driven nodal surface superconductivity of Fermi arcs

According to recent observations, the topological surface states of Weyl semimetals may develop a superconducting gap, while bulk superconductivity remains absent. What drives the formation of this novel superconducting state is an open question. Here, we show that this phenomenon can arise from the interaction of Fermi arc electrons with both surface and bulk phonons in time-reversal-invariant Weyl semimetals. We identify two competing pairing channels, intra-arc and inter-arc, whose relative strength is governed by the efficiency of Coulomb screening at the surface. The combined effect of the Fermi arcs being disconnected and the weak screening of the Coulomb repulsion at the system's surface causes nodes to appear in the superconducting gap, as observed recently by photoelectron spectroscopy experiments on PtBi2. This suggests manipulation of the Coulomb screening, e.g. by a surface layer coating, as a pathway to engineer the critical temperature, as well as size and symmetry of the surface superconducting gap.