Frustration phenomena in Josephson point contacts between single-band and three-band superconductors

TL;DR

This paper investigates the Josephson effect in point contacts between single-band and three-band superconductors, revealing frustration phenomena and current-phase relations that depend on temperature and time-reversal symmetry, aiding the detection of BTRS states.

Contribution

It provides a general expression for the Josephson current in such contacts and analyzes the effects of broken time-reversal symmetry on current-phase relations.

Findings

Frustration phenomena occur in BTRS three-band superconductors.

Near the critical temperature, current-phase relations are close to sinusoidal.

At very low temperatures, multiple ground states can exist in the contact.

Abstract

Within the formalism of Usadel equations the Josephson effect in dirty point contacts between single-band and three-band superconductors is investigated. The general expression for the Josephson current, which is valid for arbitrary temperatures, is obtained. We calculate current-phase relations for very low temperature and in the vicinity of the critical temperature. For three-band superconductors with broken time-reversal symmetry (BTRS) point contacts undergo frustration phenomena with different current-phase relations, corresponding to {\phi}-contacts. For three-band superconductors without BTRS we have close to sinusoidal current-phase relations and absence of the frustration, excepting the case of very low temperature, where under certain conditions two ground states of the point contact are realized. Our results can be used as the potential probe for the detection of the possible BTRS state in three-band superconducting systems.