Enhancement of the topological regime in elongated Josephson junctions

TL;DR

This paper theoretically investigates how elongating planar Josephson junctions enhances their topological superconducting phase, facilitating the emergence of Majorana bound states and improving experimental detectability through critical current measurements.

Contribution

It demonstrates that elongation of Josephson junctions significantly broadens the topological phase range and reduces the critical magnetic field needed for the transition, aiding experimental realization.

Findings

Elongation amplifies the Zeeman-induced phase shift of Andreev bound states.

Topological phase range can be increased by junction elongation.

Critical magnetic field for topological transition decreases linearly with elongation.

Abstract

We theoretically study topological superconductivity in elongated planar Josephson junctions. In the presence of spin-orbit coupling and an in-plane magnetic field, the Josephson junction can enter the topological phase and host zero-energy Majorana bound states over a range of the superconducting phase difference centered around $\pi$, with the span of this range determined by the strength of the magnetic field. We demonstrate that the topological superconducting phase range can be greatly increased by elongation of the junction, which causes an amplification of the Zeeman-induced phase shift of Andreev bound states. We show that the appearance of trivial in-gap states that occurs in elongated junctions can prohibit the creation of Majorana modes, but it can be mitigated by further proximitization of the junction with additional superconducting contacts. The topological transition in this system can be probed by measurements of the critical current and we show that the elongation of the junction leads to a linear decrease of the transition critical magnetic field beneficial for experimental studies.