Theoretical study of the ideal electrical resistivity of simple fcc metals

Abstract

We have completed a study of the temperature dependence of the ideal electrical resistivity of simple fcc metals, with emphasis on the role deviations of the solution of the Boltzmann e$\stackrel{\mathrm{\ifmmode\acute\else\textasciiacute\fi{}}}{\mathrm{q}}$uation from the simple $cos\ensuremath{\theta}$ form employed frequently in such investigations. We consider a model for which the Fermi surface has spherical shape, but is located near the zone boundaries of an fcc crystal. The temperature dependence of the electrical resistivity has been studied with the use of the variational principle, and a solution constructed from a linear combination of up to nine cubic harmonics. This number is sufficient for the variational calculation to converge over a wide range of temperatures, except at low temperatures (\ensuremath{\lesssim}10\ifmmode^\circ\else\textdegree\fi{}K) where the umklapp processes freeze out rapidly. We examine the nature of the solution to the linearized Boltzmann equation and the temperature dependence of the electrical resistivity for three cases: (i) the Fermi surface lies entirely within the first Brillouin zone, with radius appropriate to the belly region of the copper Fermi surface; (ii) the Fermi surface just touches the zone boundary; and (iii) the Fermi surface lies outside the first zone, with radius equal to that of the free-electron sphere appropriate to aluminum.