Density expansion for transport coefficients: Long-wavelength versus Fermi surface nonanalyticities

TL;DR

This paper investigates how the conductivity in 2D quantum Lorentz models expands with scatterer density, revealing distinct nonanalytic behaviors linked to different scattering processes and identifying a specific power-law correction.

Contribution

It demonstrates that nonanalyticities in the density expansion have different forms depending on momentum transfer, highlighting a power-law correction in 2D models with point-like scatterers.

Findings

Nonanalyticities differ for small and large momentum transfers.

Leading correction to conductivity is of order n^{3/2}.

Contrast with 3D case where nonanalyticities are logarithmic.

Abstract

The expansion of the conductivity in 2-d quantum Lorentz models in terms of the scatterer density n is considered. We show that nonanalyticities in the density expansion due to scattering processes with small and large momentum transfers, respectively, have different functional forms. Some of the latter are not logarithmic, but rather of power-law nature, in sharp contrast to the 3-d case. In a 2-d model with point-like scatterers we find that the leading nonanalytic correction to the Boltzmann conductivity, apart from the frequency dependent weak-localization term, is of order n^{3/2}.