We calculate the transport relaxation time τtr and spin transport relaxation time τs,tr for a twodimensional electron gas with spatially fluctuating Rashba spin-orbit interaction. These relaxation times determine the electrical and spin conductivity of the two-dimensional system, respectively. It is shown that the transport relaxation time τtr is a nonmonotonic function of electron energy ε, whereas the spin transport relaxation time τs,tr decreases with increasing ε, similarly to the conventional electron relaxation time τ that characterizes the decay of an electron state corresponding to certain values of the momentum and spin. Such a behavior of the relaxation times leads to unusual temperature dependence of the electrical and spin conductivity.

Using the Green functions method we study transport properties of surface electrons in topological insulators in the presence of a correlated random exchange field. Such an exchange field may be due to random magnetization with correlated fluctuations. We determine the relaxation time due to scattering from the magnetization fluctuations and from other structural defects. Then we calculate the longitudinal charge conductivity taking into account the contribution due to vertex correction.

We discuss the effect of a magnetic thin-film ribbon at the surface of a topological insulator on the charge and spin transport due to surface electrons. If the magnetization in the magnetic ribbon is perpendicular to the surface of a topological insulator, it leads to a gap in the energy spectrum of surface electrons. As a result, the ribbon is a barrier for electrons, which leads to electrical resistance. We have calculated conductance of such a structure. The conductance reveal some oscillations with the length of the magnetized region due to the interference of transmitted and reflected waves. We have also calculated the Seebeck coefficient when electron flux is due to a temperature gradient.

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