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 graphenelike 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 Lambda(s) for spin-polarization decay behaves as Lambda(s) proportional to mu(-2).