Boltzmann electronic dc transport in multiorbital weakly disordered crystals

Abstract

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 noninteracting 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 semianalytical 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 disorders 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 the Drude behavior.

Resistivity anisotropy from the multiorbital Boltzmann equation in nematic FeSe

“…Indeed, as recently discussed for a generic multiorbital case in Ref. [51], while in a single-band system the transport scattering time for isotropic impurities coincides with the quasiparticle one, in a multiorbital system this is not the case. Here the multiorbital composition of the electronic bands plays a role analogous to the momentum dependence of the scattering potential for the single-band system, with two main implications.…”

“…In this case the so-called relaxation-time approximation becomes exact and Eq. ( 8) defines the transport scattering time [46,51,52,60,61]. However, for a generic band structure w and v are not necessarily parallel and one should solve explicitly Eq.…”

“…In Ref. [51] we recently proposed a semi-analytical solution to this problem. More specifically, we showed that thanks to the energy conservation implicit in the collision-integral kernel (7) the matrix 1 − Qτ becomes block-diagonal when the k vectors are ordered in groups belonging to the same energy shell.…”

“…In this paper by taking advantage of the semi-analytical solution of the multiorbital problem recently provided in Ref. [51] we will compute the dc anisotropy in FeSe testing the two nematic scenarios discussed above, where either the xy nematic order parameter (2) is included or not. We will show that in both cases the velocities renormalization due to disorder significantly contributes to the resistivity anisotropy, and becomes crucial to account for the experimental observations.…”

“…In Sec. II we discuss the Boltzmann equation for the multiorbital model in the presence of disorder and we summarize the main results of the recent theoretical derivation [51] of a semi-analytical solution of the integral equation for the renormalized velocities. In Sec.…”