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

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 φ-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.

Proximity and Josephson effects in microstructures based on multiband superconductors (Review Article)

“…The opposite case, namely, the diffusion limit of a microcontact formed by a single-band and three-band superconductor with time-reversal symmetry breaking, has been considered in Ref. 113. As in the KO-1 theory, 102 the pointcontact geometry allows to reduce the problem to onedimensional Usadel equations, generalized only to three energy gaps, in which all terms but the gradient are discarded.…”

“…Despite the presence of two possible current-phase relations in Josephson junctions, 113 the i c ¼ i c (U e /U 0 ) dependence is the same for both ground states [ Fig. 30(a)].…”

Dc SQUID based on a three-band superconductor with broken time-reversal symmetry

“…Following the notations introduced earlier about phases of contacting superconductors (see Ref. 17) we denote the phase difference on the contact between the first order parameter of a threeband superconductor and the order parameter of the single-band superconducting part of the SQUID loop as i χ , where 1, 2 i = are index of the contact. The single-valuedness of the phase differences around the loop, which are thicker than the London penetration depth for the singleand three-band superconductors, requires…”

“…Motivated by these unresolved challenges we address the problem of the dynamics of the dc SQUID with Josephson point contacts between a conventional s-wave and an isotropic dirty three-band s-wave superconductors. Using earlier obtained results on the Josephson effect in such superconducting systems [17], we investigate dependencies of the total flux in the dc SQUID from the externally applied flux (S states) and the magnetic field dependence of the critical current. We show, what new kind of features and effects for the characteristics of the dc SQUID we can expect due to the multi-band structure of the order parameter with possible manifestation of the BTRS state.…”

Josephson systems based on ballistic point contacts between single-band and multi-band superconductors

“…Previously, we investigated the Josephson effect [32] and the behavior of a dc SQUID with Josephson point contacts between an s-wave superconductor and a three-band isotropic superconductor in the dirty limit [30] We have revealed the unusual dependence of the critical current on the external magnetic flux and demonstrated the possibility of appearance of multihysteresis loops in the dependence of the total flux on the external magnetic flux. It was found that all these features of Josephson systems are associated with BTRS.…”