Two-dimensional macroscopic quantum tunneling in multi-gap superconductor Josephson junctions

TL;DR

This paper investigates macroscopic quantum tunneling in a Josephson junction combining single-gap and two-gap superconductors, revealing how different tunneling paths relate to collective modes and can serve as indicators of the Josephson-Leggett mode.

Contribution

It introduces a semi-classical method to analyze multi-dimensional quantum tunneling in a novel Josephson junction system, highlighting the role of in-phase and out-of-phase tunneling paths.

Findings

The MQT escape rate depends on the bias current and inter-band coupling.

Two tunneling paths, in-phase and out-of-phase, are identified and characterized.

The difference in escape rates can indicate the Josephson-Leggett mode presence.

Abstract

Low-temperature characters of superconducting devices yield definite probes for different superconducting phenomena. We study the macroscopic quantum tunneling (MQT) in a Josephson junction, composed of a single-gap superconductor and a two-gap superconductor. Since this junction has two kinds to the superconducting phase differences, calculating the MQT escape rate requires the analysis of quantum tunneling in a multi-dimensional configuration space. Our approach is the semi-classical approximation along a 1D curve in a 2D potential- energy landscape, connecting two adjacent potential (local) minimums through a saddle point. We find that this system has two plausible tunneling paths; an in-phase path and an out-of-phase path. The former is characterized by the Josephson-plasma frequency, whereas the latter is by the frequency of the characteristic collective mode in a two-band superconductor, Josephson- Leggett mode. Depending on external bias current and inter-band Josephson-coupling energy, one of them mainly contributes to the MQT. Our numerical calculations show that the difference between the in-phase path and the out-of-phase path is manifest, with respect to the bias- current-dependence of the MQT escape rate. This result suggests that our MQT setting be an indicator of the Josephson-Leggett mode.