Chirality and spin transformation of triplet Cooper pairs upon interaction with singlet condensate

TL;DR

This paper explores how triplet Cooper pairs with specific spin and chirality interact with singlet pairs in multiterminal Josephson junctions, leading to novel spin transformations and finite Josephson currents in three-terminal setups.

Contribution

It introduces the concept of chirality in polarized triplet Cooper pairs and analyzes their interaction with singlet pairs in complex Josephson junctions, revealing new current behaviors.

Findings

Finite Josephson current appears only in three-terminal junctions.

Triplet pairs can change spin and chirality upon interaction with singlet pairs.

The Josephson current depends on the phases of the superconductors.

Abstract

We show that the fully polarized triplet s-wave component is characterized not only by the spin direction, but also by chirality. Interaction of a polarized triplet component and a singlet one results in creation of triplet Cooper pairs with opposite spin direction or of different chiralities. Such spin transformation leads to interesting phenomena in multiterminal magnetic Josephson junctions. We calculate the dc Josephson current $I_{\text{J}}$ in a multiterminal Josephson contact of the S$_{\text{m}}$/n/S$_{\text{m}}^{\prime}$ type with "magnetic" superconductors S$_{\text{m}}$ that generate fully polarized triplet components. The superconductors S$_{\text{m}}$ are attached to magnetic insulators (filters) which let to pass electrons with a fixed spin direction only. The filter axes are assumed to be oriented antiparallel to each other. The Josephson current is zero in two-terminal Josephson junction, i.e., in S/n/S$_{\text{m}}$ or in S$_{\text{m}}$/n/S$_{\text{m}}^{\prime}$ contact. But in the three-terminal Josephson junction, with another S superconductor attached to the normal wire, the finite current $I_{\text{J}}$ appears flowing from the S~superconductor to S$_{\text{m}}$ superconductors. The currents through the right (left) superconductors S$_{\text{m}}$ are opposite in sign, ${I_{\text{R}} \equiv I_{\text{J}} = I_{\text{c}} \sin (\chi_{\text{R}} + \chi_{\text{L}} - 2 \chi) = - I_{\text{L}}}$, where $\chi_{\text{L/R}}$ and $\chi$ are the phases of superconductors S$_{\text{m}}$, S$_{\text{m}}^{\prime}$, and S, respectively. We discuss possibilities of experimental observation of the effect.