Motivated by the increasing number of systems featuring multiple bands at low energy, we address the Boltzmann approach to transport in a multiband weakly disordered non-interacting crystal subject to a small electric field. In general, the multiband structure leads to a considerable complication of the Boltzmann equation. Indeed, even in the presence of elastic impurity scattering one needs to compute for each band and momentum the dressed velocities, which account for scattering events. Here we provide a semi-analytical solution to the Boltzmann equation that reduces such a challenging numerical task to the much simpler numerical computation of a small tensor whose dimension is set by the number of bands at the Fermi level. This approach further allows us to discuss the interplay of symmetry and disorder for different impurity types, including those originating from random-matrix Wigner ensembles. As an example of application we consider the 2D isotropic Rashba metal and we discuss, in a full analytical fashion, how different types of disorder may break the exactness of the relaxation-time approximation and induce transport anisotropy, and may allow one to identify the presence of spin-orbit coupling as deviations of the conductivity from Drude behavior.
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