Phonon-mediated intrinsic topological superconductivity in Fermi arcs

TL;DR

This paper demonstrates that phonons can induce topological superconductivity on the surface of Weyl semimetals, resulting in chiral p-wave pairing and Majorana states, with implications for nonlocal electron-phonon interactions.

Contribution

It introduces a model showing phonon-mediated topological superconductivity on Weyl semimetal surfaces, highlighting nonlocal electron-phonon effects and surface-dominant pairing.

Findings

Surface superconductivity dominates over bulk in certain chemical potential ranges.

The superconducting gap exhibits a layer-dependent suppression due to nonlocal electron-phonon coupling.

Majorana bound states can form in vortex cores on the Fermi arcs.

Abstract

We propose that phonons can intrinsically mediate topological superconductivity on the surface of Weyl semimetals. Weyl semimetals are gapless topological materials with nondegenerate zero energy surface states known as Fermi arcs. We derive the phonon spectrum and electron-phonon coupling in an effective model of a Weyl semimetal and apply weak-coupling Bardeen-Cooper-Schrieffer theory of superconductivity. In a slab geometry, we find that surface superconductivity dominates over bulk superconductivity in a range of chemical potentials around the Weyl nodes. The superconducting gap function realizes spinless chiral $p$-wave Cooper pairing in the Fermi arcs, leading to Majorana bound states in the core of vortices. Furthermore, we find a suppression of the absolute value of the gap in the center of the Fermi arcs, which is not captured by a local Hubbard attraction. The suppression is due to the nonlocal origin of electron-phonon coupling, leading to a layer dependence which has important consequences for topological surface states.