Spin Transport in Fractal Conductors With the Rashba Spin-Orbit Coupling

Abstract

Spatial behavior of spin transport in a Sierpinski gasket fractal subject to the Rashba spin-orbital coupling is studied from two dimensions to a quasi-one dimensional arrangement. We represent two normal metal leads by a self-energy matrix, discretize the derived continuous Hamiltonian in the tight-binding approximation, and apply the LandauerÀKeldysh formalism to the nonequilibrium transport. It is observed that the spin Hall e®ect present in the resultant distribution of spin density critically depends on the fractal structure and the shape of the thin¯lm. The local spin density and transmission are numerically computed for both fractal and nonfractal thin¯lms varying from a two dimensional square lattice into a quasi-one dimensional fractal shape. Spin lter e®ect is observed from the asymmetrical geometrical shape of Sierpinski triangle and pure spin current can be derived at appropriate conditions.