Critical current for an insulating regime of an underdamped current-biased topological Josephson junction

TL;DR

This paper analytically investigates the critical current in a topological Josephson junction, revealing a transition governed by quasiparticle tunneling and the influence of Majorana bound states on the insulating-conducting transition.

Contribution

It introduces a simplified model for topological Josephson junctions at zero temperature, highlighting the role of Majorana states and their hybridization in the transition behavior.

Findings

Lower critical current for transition due to quasiparticle tunneling

Exponential increase in critical current with finite system length

Experimental signatures of Majorana states via critical current measurements

Abstract

We study analytically an underdamped current-biased topological Josephson junction. First, we consider a simplified model at zero temperature, where the parity of the non-local fermionic state formed by Majorana bound states (MBSs) localized on the junction is fixed, and show that a transition from insulating to conducting state in this case is governed by single-quasiparticle tunneling rather than by Cooper pair tunneling in contrast to a non-topological Josephson junction. This results in a significantly lower critical current for the transition from insulating to conducting state. We propose that, if the length of the system is finite, the transition from insulating to conducting state occurs at exponentially higher bias current due to hybridization of the states with different parities as a result of the overlap of MBSs localized on the junction and at the edges of the topological nanowire forming the junction. Finally, we discuss how the appearance of MBSs can be established experimentally by measuring the critical current for an insulating regime at different values of the applied magnetic field.