Macroscopic quantum tunneling in multigap superconducting Josephson junctions: Enhancement of escape rate via quantum fluctuations of the Josephson-Leggett mode

We theoretically study the macroscopic quantum tunneling (MQT) in a hetero Josephson junction formed by a conventional single-gap superconductor and a multigap superconductor such as iron-based superconductors and MgB ₂. In such a Josephson junction more than one phase difference is defined. We clarify their phase dynamics and construct a theory for the MQT in the multigap Josephson junctions. The dynamics of the phase differences are strongly affected by the Josephson-Leggett mode, which is the out-of-phase oscillation mode of the phase differences. The escape rate is calculated in terms of the effective action renormalized by the Josephson-Leggett mode at zero-temperature limit. We successfully predict drastic enhancement of the escape rate when the frequency of the Josephson-Leggett mode is less than the Josephson-plasma frequency.