Spin relaxation, diffusion, and Edelstein effect in chiral metal surface

Abstract

We study electron spin transport at spin-splitting surface of chiral-crystalline-structured metals and Edelstein effect at the interface, by using the Boltzmann transport equation beyond the relaxation time approximation. We first define spin relaxation time and spin diffusion length for two-dimensional systems with anisotropic spin--orbit coupling through the spectrum of the integral kernel in the collision integral. We then explicitly take account of the interface between the chiral metal and a nonmagnetic metal with finite thickness. For this composite system, we derive analytical expressions for efficiency of the charge current--spin current interconversion as well as other coefficients found in the Edelstein effect. We also develop the Onsager's reciprocity in the Edelstein effect along with experiments so that it relates local input and output, which are respectively defined in the regions separated by the interface. We finally provide a transfer matrix corresponding to the Edelstein effect through the interface, with which we can easily represent the Onsager's reciprocity as well as the charge--spin conversion efficiencies we have obtained. We confirm the validity of the Boltzmann transport equation in the present system starting from the Keldysh formalism in the supplemental material. Our formulation also applies to the Rashba model and other spin-splitting systems.