Localization and spin transport in honeycomb structures with spin-orbit coupling

Transfer-matrix methods are used for a tight-binding description of electron transport in graphene-like geometries, in the presence of spin-orbit couplings. Application of finite-size scaling and phenomenological renormalization techniques shows that, for strong enough spin-orbit interactions and increasing on-site disorder, this system undergoes a metal-insulator transition characterized by the exponents $\nu =2.71(8)$, $\eta =0.174(2)$. We show how one can extract information regarding spin polarization decay with distance from an injection edge, from the evolution of wave-function amplitudes in the transfer-matrix approach. For (relatively weak) spin-orbit coupling intensity $\mu$, we obtain that the characteristic length ${\mathrm{\Lambda }}_s$ for spin-polarization decay behaves as ${\mathrm{\Lambda }}_s\propto {\mu }^{-2}$.