Spin-polarized Josephson and quasiparticle currents in superconducting spin-filter tunnel junctions

We present a theoretical study of the effect of spin filtering on the Josephson and dissipative quasiparticle currents in a superconducting tunnel junction. By combining the quasiclassical Green's functions and the tunneling Hamiltonian method, we describe the transport properties of a generic junction consisting of two superconducting leads with an effective exchange field $\mathbf{h}$ separated by a spin-filter insulating barrier. We show that in addition to the tunneling of Cooper pairs with total spin projection $S_z=0$ there is another contribution to the Josephson current due to triplet Cooper pairs with total spin projection $S_z\ne 0$. The latter is finite and not affected by the spin-filter effect provided that the fields $\mathbf{h}$ and the magnetization of the barrier are noncollinear. We also determine the quasiparticle current for a symmetric junction and show that the differential conductance may exhibit peaks at different values of the voltage depending on the polarization of the spin filter, and the relative angle between the exchange fields and the magnetization of the barrier. Our findings provide a plausible explanation for existing experiments on Josephson junctions with magnetic barriers, predict further effects, and show how spin-polarized supercurrents in hybrid structures can be created.

Figure 1

The temperature dependence of the critical current for different values of $h$ and $r$. We assume that $\alpha =\beta =0$. Inset: The structure described by our model Hamiltonian Eq. (1). The black region represents the spin-filter barrier while the gray regions are layers with a finite exchange field pointing in an arbitrary direction. $d_F$ is the thickness of these layers and we have defined ${\tilde{I}}_c=2I_{c}e{R}_N/\left({\Delta }_0\pi \right)$, where ${\Delta }_0$ is the value of the order parameter at $T=0$ and $h=0$.

Figure 2

The temperature dependence of ${\tilde{I}}_c$ for different values of $r$ and $\alpha =\pi /2$ (a); and for different values of $\alpha$ and $r=0.1$ (b). In both panels $h=0.567{\Delta }_0$.

Figure 3

The zero-temperature normalized differential conductance $G_{qp}=R_{N}d{I}_{qp}/dV$ for $h=0.4{\Delta }_0$ and $r=0,0.5,1$. Left panel: $\alpha =\beta =\pi /4$; right panel: $\alpha =0$, $\beta =\pi$. In calculating the curves we have added a small $\eta =0.01{\Delta }_0$ damping factor. Note that the curves are shifted vertically for clarity.