Boltzmann Equations for Spin and Charge Relaxations in Superconductors

Abstract

In a superconductor coupled with a ferromagnetic metal, spin and charge imbalances can be induced by injecting spin-polarized electron current from the ferromagnetic metal. We theoretically study a nonequilibrium distribution of quasiparticles in the presence of spin and charge imbalances. We show that four distribution functions are needed to characterize such a nonequilibrium situation, and derive a set of linearized Boltzmann equations for them by extending the argument by Schmid and Schön based on the quasiclassical Green's function method. Using the Boltzmann equations, we analyze the spin imbalance in a thin superconducting wire weakly coupled with a ferromagnetic electrode. The spin imbalance induces a shift $δμ$ ($- δμ$) of the chemical potential for up-spin (down-spin) quasiparticles. We discuss how $δμ$ is relaxed by spin-orbit impurity scattering.