Electrical Conductivity of Interacting Fermions. II. Effects of Normal Scattering Processes in the Presence of Umklapp Scattering Processes

The electrical resistivity due only to mutual Coulomb interaction of the d -dimensional lattice electron systems ( d ≥2) in the presence of Umklapp scattering processes is studied on the basis of the Fermi liquid theory. It is shown that normal scattering processes generally contribute to the resistivity if Umklapp scattering processes are present. This fact gives a natural explanation of the resistivity of the d =∞ Hubbard model which is determined only by the damping rate of quasi-particles, γ. In the case of d =2, however, it is shown that the resistivity is proportional to T 2 , T being the temperature, even when normal scattering processes, which give T 2 log T -contribution to γ, contribute to the resistivity. In the special case of the square lattice, where the transfer integrals are only between the nearest neighbors, the coefficient of the T 2 -term in the second order of the interaction is shown to diverge as (1/δ) log (1 / δ) when δ→0, δ being the doping rate away from half-filling.