Diffusive density response of electrons in anisotropic multiband systems

TL;DR

This paper calculates the anisotropic electron density response in multiband systems with impurities, emphasizing the importance of direction-dependent vertex corrections and relaxation times for understanding transport in topological materials.

Contribution

It provides a detailed method to compute the diffusive density response considering anisotropy and impurity effects, offering new empirical rules for diffusion constants in complex materials.

Findings

Direction-dependent vertex corrections are essential for accurate diffusion constants.

Component-wise transport relaxation times significantly influence anisotropic transport properties.

Empirical rules help interpret diffusion behavior in topological and anisotropic systems.

Abstract

We explicitly calculate the density-density response function with conserving vertex corrections for anisotropic multiband systems in the presence of impurities including long-range disorder. The direction-dependence of the vertex corrections is correctly considered to obtain the diffusion constant which is given by the combination of the componentwise transport relaxation times and velocities on the Fermi surface. We also investigate the diffusive density response of various anisotropic systems, propose some empirical rules for the corresponding diffusion constant, and demonstrate that it is crucial to consider the component-dependence of the transport relaxation times to correctly interpret the transport properties of anisotropic systems, especially various topological materials with a different power-law dispersion in each direction.