Spin filtration in generalized Sierpinski triangles in presence of Rashba spin–orbit interaction

Abstract

In this work, we theoretically investigate the phenomenon of spin polarization in generalized Sierpinski gasket (SPG) triangles (, , , ) in the presence of Rashba spin–orbit interaction (RSOI) within a tight-binding framework. The geometrical construction is addressed for all four types of generalized SPG triangles using an iterative function system that begins with a fixed triangle of any arbitrary side length. The geometry of various types of fractal networks has a major impact on the degeneracy of the energy spectrum. It is shown that only the two-terminal setup in the presence of RSOI is incapable of breaking the spin degeneracy, which necessitates the use of a three-terminal setup to break the time-reversal symmetry. The effect of flip map induced anisotropic hopping integrals on three-terminal spin-resolved transmission probabilities is studied. In several cases, we find almost spin polarization in our considered lattices. We also analyze how spin polarization varies with RSOI strength and fractal generations. Our results indicate that fractal lattices might be suitable functional elements for designing future spin-based electronic devices.