Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions

TL;DR

This paper investigates how Joule overheating affects the fractional ac Josephson effect in topological Josephson junctions, revealing thermal poisoning as a key factor in the partial suppression of odd Shapiro steps and providing evidence for Majorana bound states.

Contribution

It introduces a modified resistively shunted junction model showing thermal effects explain the incomplete suppression of odd Shapiro steps in topological junctions.

Findings

Thermal poisoning explains the resilience of higher order odd Shapiro steps.

Residual supercurrent at Shapiro node gaps indicates Majorana bound state contribution.

Thermal effects are crucial in interpreting topological Josephson junction experiments.

Abstract

Topological Josephson junctions designed on the surface of a 3D-topological insulator (TI) harbor Majorana bound states (MBS's) among a continuum of conventional Andreev bound states. The distinct feature of these MBS's lies in the $4\pi$-periodicity of their energy-phase relation that yields a fractional ac Josephson effect and a suppression of odd Shapiro steps under $r\!f$ irradiation. Yet, recent experiments showed that a few, or only the first, odd Shapiro steps are missing, casting doubts on the interpretation. Here, we show that Josephson junctions tailored on the large bandgap 3D TI Bi$_2$Se$_3$ exhibit a fractional ac Josephson effect acting on the first Shapiro step only. With a modified resistively shunted junction model, we demonstrate that the resilience of higher order odd Shapiro steps can be accounted for by thermal poisoning driven by Joule overheating. Furthermore, we uncover a residual supercurrent at the nodes between Shapiro lobes, which provides a direct and novel signature of the current carried by the MBS. Our findings showcase the crucial role of thermal effects in topological Josephson junctions and lend support to the Majorana origin of the partial suppression of odd Shapiro steps.