Flux-driven and geometry-controlled spin filtering for arbitrary spins in aperiodic quantum networks*

We demonstrate that an aperiodic array of certain quantum networks comprising magnetic and nonmagnetic atoms can act as perfect spin filters for particles with arbitrary spin state.This can be achieved by introducing minimal quasi-one dimensionality in the basic structural units building up the array, along with an appropriate tuning of the potential of the non-magnetic atoms,the tunnel hopping integral between the non-magnetic atoms and the backbone, and, in some cases,by tuning an external magnetic field.The proposed networks have close resemblance with a family of recently developed photonic lattices,and the scheme for spin filtering can thus be linked, in principle,to a possibility of suppressing any one of the two states of polarization of a single photon, almost at will.We use transfer matrices and a real space renormalization group scheme to unravel the conditions under which any aperiodic arrangement of such topologically different structures will filter out any given spin projection following an energy-independent commutation of the transfer matrices.Our results are analytically exact,and corroborated by extensive numerical calculations of the spin polarized transmission and the density of states of such systems.