Inelastic Coulomb scattering in a two-band picture and the temperature dependence of the resistivity

A calculation of the inelastic lifetime and the resistivity resulting from Coulomb coupling of conduction (‘‘s’’) electrons to a narrow (‘‘d’’) band is given for both the regular and the pair-transfer interactions in the ballistic regime. It is shown that in all cases for overlapping bands the scattering rate and the resistivity behave as ${\mathit{T}}^2$ for a three-dimensional electron gas and as ${\mathit{T}}^2$ lnT at two dimensions. This is the same temperature dependence as found for Coulomb scattering in a single band, but its contribution to the resistivity does not necessitate umklapp processes. The result contradicts recent arguments leading to a linear temperature dependence in a two-band picture at two dimensions. The latter can be obtained when a small amount of scattering by defects is added, as known for the single-band case. It is argued that such a linear contribution to the temperature-dependent resistivity may be more pronounced in the two-band case. Experimental manifestations of the results are discussed.