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We theoretically study the macroscopic quantum tunneling (MQT) in a heteroJosephson junction formed by a conventional single-gap superconductor and amulti-gap one such as ${MgB}_{2}$ and iron-based superconductors. In such aJosephson junction more than one phase differences are defined. We clarify thequantum dynamics of the phase differences and construct a theory for the MQT inthe multi-gap Josephson junctions. The dynamics of the phase differences arestrongly affected by the Josephson-Leggett mode, which is the out-of-phaseoscillation mode of the phase differences. The escape rate is calculated interms of the effective action renormalized by the Josephson-Leggett mode. It isshown that the escape rate is drastically enhanced when the frequency of theJosephson-Leggett mode is less than the Josephson-plasma frequency.

physical review. b, condensed matter and materials physics

Macroscopic quantum tunneling in multigap superconducting Josephson  junctions: Escape rate enhancement via quantum fluctuations of  Josephson-Leggett mode