Using Josephson junctions to determine the pairing state of superconductors without crystal inversion symmetry

TL;DR

This paper investigates how Josephson junctions can be used to identify the pairing symmetry in non-centrosymmetric superconductors, providing theoretical models and numerical results for different orientations and pairing states.

Contribution

It introduces a theoretical framework for analyzing Josephson junctions with antisymmetric spin-orbit coupling, linking junction behavior to the superconductor's pairing symmetry and crystal orientation.

Findings

Josephson current varies with crystallographic orientation

Differential conductance reveals pairing state characteristics

Critical current depends on singlet and triplet pairing weights

Abstract

Theoretical studies of a planar tunnel junction between two superconductors with antisymmetric spin-orbit coupling are presented. The half-space Green's function for such a superconductor is determined. This is then used to derive expressions for the dissipative current and the Josephson current of the junction. Numerical results are presented in the case of the Rashba spin-orbit coupling, relevant to the much studied compound CePt$_3$Si. Current-voltage diagrams, differential conductance and the critical Josephson current are presented for different crystallographic orientations and different weights of singlet and triplet components of the pairing state. The main conclusion is that Josephson junctions with different crystallographic orientations may provide a direct connection between unconventional pairing in superconductors of this kind and the absence of inversion symmetry in the crystal.