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 nonmagnetic atoms, the tunnel hopping integral between the nonmagnetic atoms, and the backbone, and, in some cases, by tuning an external magnetic field. This latter result opens up the interesting possibility of designing a flux-controlled spin demultiplexer using quantum networks. 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 the 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. The filtering turns out to be engineered by an energy-independent commutation of the basic transfer matrices, which results out of a unique set of correlation between the system parameters and/or the external flux. The commutation generates absolutely continuous subbands populated by extended, Bloch-like eigenstates in the densities of states, even for such aperiodic systems, thus defying localization and creating unattenuated transport over a continuous range of energy eigenvalues. This is an example which goes well beyond the previous studies on disordered systems, where delocalization of single particle excitations could be achieved by resonance, but only for a finite set of energy eigenvalues of the system. Our results are analytically exact, and corroborated by extensive numerical calculations of the spin-polarized transmission and the density of states of such systems.

• Received 6 March 2018
• Revised 11 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.075415