Spin Josephson effect in topological superconductor-ferromagnet junction

Abstract

The composite topological superconductor (TS), made of one-dimensional spin-orbit coupled nanowire with proximity-induced s-wave superconductivity, is not a pure p-wave superconductor but still has a suppressed s-wave pairing. We propose to probe the spin texture of the p-wave pairing in this composite TS by examining possible spin supercurrents in an unbiased TS/ferromagnet junction. It is found that both the exchange-coupling induced and spin-flip reflection induced spin currents exist in the setup and survive even in the topological phase. We showed that besides the nontrivial p-wave pairing state accounting for Majorana Fermions, there shall be a trivial p-wave pairing state that contributes to spin supercurrent. The trivial p-wave pairing state is diagnosed from the mixing effect between the suppressed s-wave pairing and the topologically nontrivial p-wave pairing. The d vector of the TS is proved not to be rigorously perpendicular to the spin projection of p-wave pairings. Our findings are also confirmed by the Kitaev's p-wave model with a nonzero s-wave pairing.