Josephson effect in a Weyl SNS junction

TL;DR

This paper calculates the Josephson current in a Weyl superconductor-normal-metal-superconductor junction, revealing how different pairing mechanisms affect the current's dependence on chemical potential and junction conductivity.

Contribution

It introduces a model for Weyl SNS junctions with broken time-reversal symmetry and compares the effects of BCS-like and FFLO-like pairing mechanisms on the Josephson current.

Findings

Josephson current is proportional to normal-state conductivity.

BCS-like pairing current is independent of chemical potential.

FFLO-like pairing current depends on chemical potential.

Abstract

We calculate the Josephson current density j(phi) for a Weyl superconductor--normal-metal--superconductor junction for which the outer terminals are superconducting Weyl metals and the normal layer is a Weyl (semi)metal. We describe the Weyl (semi)metal using a simple model with two Weyl points. The model has broken time-reveresal symmetry, but inversion symmetry is present. We calculate the Josephson current for both zero and finite temperature for the two pairing mechanisms inside the superconductors that have been proposed in the literature, zero-momentum BCS-like pairing and finite-momentum FFLO-like pairing, and assuming the short-junction limit. For both pairing types we find that the current is proportional to the normal-state junction conductivity, with a proportionality coefficient that shows quantitative differences between the two pairing mechanisms. The current for the BCS-like pairing is found to be independent of the chemical potential, whereas the current for the FFLO-like pairing is not.