ac Josephson effect in superconducting d-wave junctions

TL;DR

This paper provides a theoretical analysis of the ac Josephson effect in d-wave superconductor junctions, revealing unique features like negative differential conductance, zero-bias peaks, and frequency doubling due to the d-wave order parameter's sign change.

Contribution

It offers a comprehensive theoretical framework for understanding ac Josephson effects in d-wave superconducting junctions, including the impact of orientation, barrier strength, and temperature.

Findings

Presence of negative differential conductance due to mid-gap states

Zero-bias conductance peaks from multiple Andreev reflections

Suppression or absence of odd ac components leading to frequency doubling

Abstract

We study theoretically the ac Josephson effect in superconducting planar d-wave junctions. The insulating barrier assumed to be present between the two superconductors may have arbitrary strength. Many properties of this system depend on the orientation of the d-wave superconductor: we calculate the ac components of the Josephson current. In some arrangements there is substantial negative differential conductance due to the presence of mid-gap states. We study how robust these features are to finite temperature and also comment on how the calculated current-voltage curves compare with experiments. For some other configurations (for small barrier strength) we find zero-bias conductance peaks due to multiple Andreev reflections through midgap states. Moreover, the odd ac components are strongly suppressed and even absent in some arrangements. This absence will lead to a doubling of the Josephson frequency. All these features are due to the d-wave order parameter changing sign when rotated $90^{\circ}$. Recently, there have been several theoretical reports on parallel current in the d-wave case for both the stationary Josephson junction and for the normal metal-superconductor junction. Also in our case there may appear current density parallel to the junction, and we present a few examples when this takes place. Finally, we give a fairly complete account of the method used and also discuss how numerical calculations should be performed in order to produce current-voltage curves.