Nonintegral Flux Trapping in Frustrated Josephson Networks of Triplet Superconductors

TL;DR

This paper explores how anisotropic coupling in Josephson networks of triplet superconductors causes frustrated $d$ vector textures, leading to spontaneous currents and fractional flux trapping, revealing new ways to engineer such systems.

Contribution

It introduces a mechanism for nonintegral flux trapping in frustrated Josephson networks with triplet pairing, highlighting the role of $d$ vector textures and geometric phases.

Findings

Frustrated Josephson networks can support spontaneous currents.

Fractional flux trapping occurs due to $d$ vector textures.

Support for $ ext{pi}$-flux trapping above a critical antisymmetric coupling.

Abstract

In a Josephson junction network, anisotropic coupling between spin triplet pairing correlations can lead to frustrated $d$ vector textures that support spontaneous Josephson currents and nonintegral flux trapping. Such networks can appear in superconducting polycrystals, as well as single-crystal superconductors. In analogy to classical spin systems, in which the presence of geometric frustration and anisotropic superexchange can lead to nontrivial spin textures, Josephson networks with anisotropic Josephson couplings cannot simultaneously optimize their $\mathrm{U}(1)$ superconducting phase difference and relative $d$ vector orientations. The internal pairing structure of Cooper pairs twists as they tunnel across the Josephson junction, and the $d$ vector texture enters as an emergent geometric phase which can spontaneously trap fractional flux. For unitary triplet pairing order, this mechanism can support $\pi$-flux trapping above a critical value of antisymmetric Josephson coupling, and is distinct from usual half-quantum vortices. The results of this work reveal new routes to engineer frustrated Josephson networks from the interplay of magnetic textures and spin triplet superconducting pairing order.