Tunable effective length of fractional Josephson junctions

TL;DR

This paper introduces a method to effectively extend the length of topological Josephson junctions by coupling to additional channels or quantum dots, enabling the study of long junction phenomena in shorter devices.

Contribution

It proposes a tunable approach to modify the effective length of topological Josephson junctions using coupling parameters, supported by analytical and numerical models.

Findings

Critical current varies with coupling strength and parity-changing perturbations.

Effective long junction behavior can be achieved in short junctions through coupling.

Numerical models confirm analytical predictions of critical current behavior.

Abstract

Topological Josephson junctions (TJJs) have been a subject of widespread interest due to their hosting of Majorana zero modes. In long junctions, i.e. junctions where the junction length exceeds the superconducting coherence length, TJJs manifest themselves in specific features of the critical current. Here we propose to couple the helical edge states mediating the TJJ to additional channels or quantum dots, by which the effective junction length can be increased by tunable parameters associated with these couplings, so that such measurements become possible even in short junctions. Besides effective low-energy models that we treat analytically, we investigate realizations by a Kane-Mele model with edge passivation and treat them numerically via tight binding models. In each case, we explicitly calculate the critical current using the Andreev bound state spectrum and show that it differs in effective long junctions in the cases of strong and weak parity changing perturbations (quasiparticle poisoning).