Self-consistent surface superconductivity in time-reversal symmetric Weyl semimetals

TL;DR

This paper introduces a variational method to analyze how surface and bulk superconductivity interact in Weyl semimetals, revealing unique features of surface superconductivity influenced by the topological surface states.

Contribution

It presents a novel variational approach to study surface-bulk superconductivity interplay in Weyl semimetals with topological surface states.

Findings

Surface superconducting gap varies with surface momentum.

Penetration length of the order parameter depends on temperature.

Surface superconductivity exhibits characteristic features due to topological states.

Abstract

Weyl semimetals host topologically protected surface states, the so-called Fermi arcs, that have a penetration depth into the bulk that depends on surface-momentum, and diverges at the Weyl points. It has recently been observed in PtBi$_2$ that such Fermi arc states can become superconducting, with a critical temperature larger than that of the bulk. Here we introduce a general variational method that captures the interplay between surface and bulk superconductivity, for any bulk Hamiltonian that harbors (topological) surface states with varying penetration depth. From the self-consistent solutions we establish that the surface state localization length of Weyl semimetals leads to characteristic features in the surface superconductivity, with a gap depending on surface momentum and a penetration length for the order parameter that is temperature-dependent due to competition with the bulk superconductivity.