Viscosity contribution to the impurity resistivity of metals by means of the current-density functional theory

Within the time-dependent density functional theory formalism we relate the impurity resistivity $\rho$ of a metal to the friction coefficient $Q$ of the metal for the same impurity moving with the infinitesimally small velocity, i.e., $ \rho=n_i Q / n_e^2 \, (1), $ where $n_i$ and $n_e$ are the concentrations of the randomly distributed impurities and the valence electrons, respectively. While Eq.(1) occurs trivial within the single-particle theory with the scattering at the {\em statically} screened impurities, its general validity within the many-body theory with the {\em dynamical} exchange and correlation included presents a progress. We utilize results [1,2] on $Q$ of the electron liquid to put the electron-electron scattering contribution into the terms of the viscosity coefficients [3]. Calculations of the residual resistivity of aluminum as a function of the atomic number of the impurity are performed, improving the agreement with experiment compared to the single- particle theory [4]. \noindent [1].V. U. Nazarov, J. M. Pitarke, C. S. Kim, and Y. Takada, Phys. Rev. B {\bf 71}, 121106(R) (2005). \noindent [2].V. U. Nazarov, J. M. Pitarke, Y. Takada, G. Vignale, and Y.-C. Chang, Phys. Rev. B {\bf 76}, 205103 (2007). \noindent [3].G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. {\bf 79}, 4878 (1997). \noindent [4].M. J. Puska and R. M. Nieminen, Phys. Rev. B {\bf 27}, 6121 (1983).