  Spatial behavior of spin transport in a Sierpinski gasket fractal is studied
from two dimensions to quasi-one dimension subject to the Rashba spin-orbital
coupling. With two normal metal leads represented by self-energy matrix,
discretizing the derived continuous Hamiltonian to a tight-binding version,
Landauer-Keldysh formalism for nonequilibrium transport can be applied. It was
observed that the spin Hall effect presents in the distribution of spin density
critically depends on the fractal structure and the shape of the thinfilm. The
local spin density and transmission are numerically tested by the present
quantum transport calculation for the fractal and non-fractal thinfilm varying
from two-dimensional square-lattice into quasi-one dimensional fractal shape
(Sierpinski triangles).
