Resonant spin Hall effect in a nanoribbon of a spin-orbit coupled electronic system

We present a theoretical study of spin Hall phenomena in a nanoribbon made of a two-dimensional square lattice with Rashba and Dresselhaus spin-orbit coupling. We show that the nanoribbon can give rise to a number of additional spin degeneracy points as well as anti-crossing points, apart from the $Γ$ point, between two nearest sub-bands. We compute the spin Hall conductivity and demonstrate that it diverges and gives rise to a resonance when chemical potential passes through those spin-degenerate or anti-crossing points. Contrary to the previous studies, here such resonance emerges even without any external perturbation like magnetic field or light. In addition, we examine the influence of anisotropy in Rashba and Dresselhaus interactions, as well as finite-temperature effects, and show that the inter subband resonance remains robust. Finally, we also investigate the signature of such additional spin degeneracy and anti-crossing points in the longitudinal conductance by using retarded Green function approach in lattice model. The peculiar features of the bands are reflected in the longitudinal conductance, which takes quantized values of 2n e²/h, where n denotes the number of bands occupied by the chemical potential with each band having spin split sub-bands.