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 $n^{3/2}$.

• Received 15 October 1996

DOI:https://doi.org/10.1103/PhysRevLett.78.2768