Influence of the spatial fluctuations of the Rashba field and magnetization on the electron and spin transport in 2D systems

In a general case, spin-orbit coupling contains regular (spatially uniform, periodic) and a random component. Local imperfections, such as a random distribution of donors or impurities, may lead to local modifications of the spin-orbit coupling. Similarly, magnetization in the system may reveal spatial fluctuations as well. Such fluctuations modify transport properties of the system and induce a variety of observable effects [Physica E 42, 2157 (2010); Nat. Phys.12, 920(2016)].
We will present the theoretical description of the selected transport characteristics (electric and spin conductivity and anomalous Hall effect) induced or modified due to the presence of random Rashba field or magnetization fluctuations in 2D systems such as semiconductor heterostructures or topological insulators. We will show an important role of the transport relaxation time for charge and spin currents, that leads to a nontrivial temperature dependence of the conductivity [S.Kudla et al., PRB 97, 245307(2018)]. We will also consider the influence of magnetization fluctuations on the anomalous Hall effect in topological insulators.