# Proximity-reduced range of internal phase differences in double Josephson junctions with closely spaced interfaces

## TL;DR

This paper investigates how proximity and pair breaking effects influence the internal phase difference range in symmetric double Josephson junctions with closely spaced interfaces, affecting supercurrent behavior as the central lead's length varies.

## Contribution

It reveals how decreasing the lead length L reduces the phase difference range and eliminates higher energy modes, leading to a conventional current-phase relation.

## Key findings

- Range of phase differences decreases with smaller L
- Higher energy modes are eliminated as L decreases
- Single junction behavior is restored at very small L

## Abstract

A substantial influence of the proximity and pair breaking effects on the range of internal phase differences is shown to take place in symmetric double Josephson junctions with closely spaced interfaces and to affect the evolution of the supercurrent j with the changing central lead's length L. If the phase difference phi between the external leads is controlled and L exceeds a few coherence lengths, the regime of interchanging modes is established. The range of the phase differences across the two individual interfaces is reduced with decreasing L, and the states of the higher energy mode are gradually eliminated. With a further decrease of L the regime of interchanging modes is destroyed along with the asymmetric mode. The conventional single junction current-phase relation j(phi) is eventually established and the condensate states' doubling is fully removed at very small L.