Spin-dependent transmission with Rashba interaction through a quantum wire with a side-coupled quantum-dot array

The non-equilibrium Greenʹs function method is applied to the system formed by a quantum-dot (QD) array side coupled to a one-dimensional quantum wire (QW), which is attached to normal leads. The system is modelled by a single-band “tight-binding” Hamiltonian with Rashba spin–orbit interaction. Using the recursive Green function method, independently of the length of the QW and the QD array, the system is reduced to a three equivalent sites with the effect of the QD array included in the central site, and the couplings to leads in the two extreme sites. Then, the transmission is studied in two cases: Firstly, when the QD array is of the same material as that of the QW and it is not magnetic, there is no preferential spin direction, and the Fano resonances and antiresonaces are analyzed as a function of the Rashba parameter and local energies in the QD array. Secondly, when the QD array is assumed to be a metallic ferromagnet, the energy of the up and down states is different and a spin-dependent transmission is obtained.