Quasiparticle poisoning effects on the dynamics of topological Josephson junctions

TL;DR

This paper investigates how quasiparticle poisoning affects the current-voltage behavior of topological Josephson junctions, proposing models to measure poisoning rates and assess junction topology even at high temperatures.

Contribution

It introduces a combined numerical and analytical approach to model quasiparticle poisoning effects within the RSJ framework, extending to long and short junction regimes.

Findings

Critical current can indicate junction topology under poisoning.

Three schemes are proposed to measure poisoning rates.

Models apply to systems with tunneling between edge states.

Abstract

The fractional Josephson effect remains one of the decisive hallmarks of topologically protected Majorana zero modes. We analyze the effects of parity violating quasiparticle poisoning onto the current voltage characteristics of topological Josephson junctions. We include poisoning events directly within the resistively shunted junction (RSJ) model in the overdamped limit both in the short- and long-junction regime. We calculate the current voltage characteristics numerically where poisoning is modeled either via additional rates in the Fokker-Planck equations or by a time dependent parity and compare them to the limits of no and strong poisoning rates which we obtain analytically. Combining the tilted washboard potential with poisoning events, we show that the critical current of the long junction limit can be used as a probe of the junction topology even in the high temperature poisoning case where relaxation- and excitation processes are equally likely. Using the tilted washboard potential model we develop three different schemes to measure the poisoning rate thereby also extending the consideration to two pairs of helical edge states containing a constriction that allows for tunneling between the two pairs of edge states.