Angular dependence of Josephson currents in unconventional superconducting junctions

TL;DR

This paper theoretically investigates how interface roughness affects Josephson currents in unconventional superconductor junctions, clarifying the applicability of the Sigrist-Rice formula in different interface conditions.

Contribution

It demonstrates that the Sigrist-Rice formula is valid for rough interfaces with diffusive regions, extending its applicability beyond ballistic cases in unconventional superconductor junctions.

Findings

SR formula works well with diffusive interfaces

It accounts for symmetric component of d-wave pair potential

Generalized formula derived for unconventional superconductors with arbitrary angular momentum

Abstract

Josephson effect in junctions between unconventional superconductors is studied theoretically within the model describing the effects of interface roughness. The particularly important issue of applicability of the frequently used Sigrist-Rice formula for Josephson current in d-wave superconductor / insulator / d-wave superconductor junctions is addressed. We show that although the SR formula is not applicable in the ballistic case, it works well for rough interfaces when the diffusive normal metal regions exist between the d-wave superconductor and the insulator. It is shown that the SR approach only takes into account the component of the d-wave pair potential symmetric with respect to an inversion around the plane perpendicular to the interface. Similar formula can be derived for general unconventional superconductors with arbitrary angular momentum l.