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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 $ν=2.71(8)$, $η=0.174(2)$. 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 $μ$, we obtain that the characteristic length $Λ_s$ for spin-polarization decay behaves as $Λ_s \propto μ^{-2}$.