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We present a study of transport in multiple-band non-interacting Fermimetallic systems based on the Keldysh formalism, taking into account theeffects of Berry curvature due to spin-orbit coupling. We apply this formalismto a Rashba 2DEG ferromagnet and calculate the anomalous Hall effect (AHE) andanisotropic magnetoresistance (AMR). The numerical calculations reproduceanalytical results in the metallic regime revealing the crossover between theskew scattering mechanism dominating in the clean systems and intrinsicmechanism dominating in the moderately dirty systems. As we increase thedisorder further, the AHE starts to diminish due to the spectral broadening ofthe quasiparticles. Although for certain parameters this reduction of the AHEcan be approximated as $\sigma_{xy}\thicksim\sigma_{xx}^{\varphi}$ with$\varphi$ varying around 1.6, this is found not to be true in general as$\sigma_{xy}$ can go through a change in sign as a function of disorderstrength in some cases. The reduction region in which the quasiparticleapproximation is meaningful is relatively narrow; therefore, a theory with awider range of applicability is called for. By considering the higher orderskew scattering processes, we resolve some discrepancies between the AHEresults obtained by using the Keldysh, Kubo and Boltzmann approaches. We alsoshow that similar higher order processes are important for the AMR when thenonvertex and vertex parts cancel each other. We calculate the AMR inanisotropic systems properly taking into account the anisotropy of thenon-equilibrium distribution function. These calculations confirm recentfindings on the unreliability of common approximations to the Boltzmannequation.

Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance