Ab inito calculation of intrinsic spin-Hall effect in graphene nanostructures

We report a theoretical analysis of intrinsic spin-Hall effect in a four-probe graphene nanostructure in the absence of spin orbit interaction and magnetic field. The nanostructure consists of a finite size graphene sheet connected to the outside world by two zigzag graphene nano-ribbons (ZGNR) and two armchair graphene nano-ribbons (AGNR), forming a cross- shaped two-dimensional device. Due to edge states induced magnetism at ZGNR boundaries, our result suggests that a pure spin-current without an accompanying charge current, is intrinsically induced giving rise to a spin-Hall effect. We have calculated the spin-Hall conductance by an atomic first principles method where density functional theory is carried out within the Keldysh nonequilibrium Green's function framework.