Spin transport in diffusive superconductors

We employ the Keldysh formalism in the quasiclassical approximation to study transport in a diffusive superconductor. The resulting $4\times 4$ transport equations describe the flow of charge and energy as well as the corresponding flow of spin and spin energy. Spin-flip scattering due to magnetic impurities is included. We find that the spin-flip length is renormalized in the superconducting case and propose an experimental system to measure the spin accumulation in a superconductor.

Figure 1

Spin battery connected to a superconductor. The thick solid line indicates a tunnel barrier.

Figure 2

Temperature dependence of $\Delta \mu ∕\mathit{eV}$. We use $R_{\mathrm{sf}}^{\left(\mathrm{S}\right)}=R^{\left(\mathrm{I}\right)}$ in the normal state. For the dotted lines $L∕l_{\mathrm{sf}}=6$, and for the solid lines $L∕l_{\mathrm{sf}}=7$. The bias $\mathit{eV}$ is $0.1\Delta (T=0)$, $3\Delta (T=0)$, $10\Delta (T=0)$ for the lower curve to the higher curve, respectively.