The Josephson effect between triplet superconductors through a finite ferromagnetic barrier

Abstract

Charge and spin transport in a junction involving two triplet superconductors and a ferromagnetic barrier are studied. We use Bogoliubov-de Gennes wavefunctions to construct the Green's function, from which we obtain the Josephson currents in terms of the Andreev reflection coefficients. We focus on the consequences of a finite barrier width for the occurrence of 0-π transitions and for the spin currents, and examine the appropriateness of the common δ-function approximation for the tunneling region.

Current-Phase Relation of a Ferromagnetic Josephson Junction Between Triplet Superconductors

“…2(c), we calculate the free energy of the junction by using Eq. (9). The unit of the free energy is given by E 0 = Φ 0 /2π.…”

Charge and spin supercurrents in triplet superconductor-ferromagnet-singlet superconductor Josephson junctions

“…We extract the current vs phase relationship by examining the summand in Eq. (21). In order to have a lowest-order Josephson effect, we require that the prod-…”

“…( 6) by comparison with the δ-function barrier, we expect our approach to be of more general validity. 21 In particular, the spin-dependent phase shifts acquired by the tunneling quasiparticles should be robust to other choices of barrier model, since they are a consequence of the orientation of the magnetization.…”

“…We extract the current vs phase relationship by examining the summand in Eq. (21). In order to have a lowest-order Josephson effect, we require that the product 7) we hence deduce that the gaps ∆ * s,k and ∆ t,k have opposite parity with respect to the z-component of the wavevector; equivalently, the gaps must have the same parity with respect to the interface momentum.…”

“…For example, the spin of the Cooper pair permits the existence of a Josephson spin current between TSs with misaligned dvectors, 14,15 similar to the spin supercurrent observed in superfluid 3 He. 16,17 Another notable proposal is the triplet superconductor-ferromagnet-triplet superconductor (TFT) junction, [18][19][20][21] where the coupling of the Cooper pairs' spin with the exchange field in the barrier causes a sign reversal of the current as the orientation of the exchange field with respect to the d-vectors is varied. This is in stark contrast to the well-known 0-π transition in magnetic junctions between SSs, [22][23][24] which is independent of the orientation of the barrier magnetization.…”