Fabry-P\'erot interference in Josephson junctions

TL;DR

This paper investigates how the Josephson current in superconductor-normal metal-superconductor junctions exhibits oscillations due to Fabry-Pérot interference, with the current's magnitude depending on the number of Andreev bound states.

Contribution

It demonstrates that Josephson current oscillations as a function of chemical potential are caused by Fabry-Pérot interference, providing a numerical analysis of Andreev bound states in such junctions.

Findings

Josephson current oscillates with chemical potential due to Fabry-Pérot interference.

Single bound state can carry more current than multiple bound states.

Current oscillations are explained by the interference condition.

Abstract

Conductance of metallic heterostructures can be controlled by applying a gate voltage to a region in the transport channel. For sufficiently long phase coherent channels, oscillations appear in conductance versus chemical potential plot, which can be explained by Fabry-P\'erot interference. In this work, we study DC Josephson effect in a superconductor-normal metal-superconductor junctions. The chemical potential of the normal metal (NM) region can be tuned by an applied gate voltage. We numerically obtain the Andreev bound states formed within the superconducting gap and calculate Josephson current by summing up the currents carried by the occupied Andreev bound states. We find that the Josephson current oscillates as a function of the chemical potential in the NM region, and these oscillations can be explained by Fabry-P\'erot interference condition. We find that Josephson current carried by one bound state can be higher than that carried by two or more bound states.