Geometrical spin manipulation in Dirac flakes

We investigate numerically the spin properties of electrons in flakes made of materials described by the Dirac equation, in the presence of intrinsic spin-orbit coupling (SOC). We show that electrons flowing along the borders of flakes via edge states become helically spin-polarized for strong SOC, for materials with and without a gap at the Fermi energy, corresponding to the massive and massless Dirac equation respectively. The helically spin-polarized electrons create spin-resolved transport, controlled by the flake's geometry in a multi-terminal device setup. A simple analytical model containing the basic ingredients of the problem is introduced to get an insight into the helical mechanism, along with our numerical results which are based on an effective tight-binding model.