Resistivity as a function of temperature for models with hot spots on the Fermi surface

Abstract

We calculate the resistivity ρ as a function of temperature T for two models currently discussed in connection with high-temperature superconductivity: nearly antiferromagnetic Fermi liquids and models with Van Hove singularities on the Fermi surface. The resistivity is calculated semiclassically by making use of a Boltzmann equation which is formulated as a variational problem. For the model of nearly antiferromagnetic Fermi liquids we construct a better variational solution compared to the standard one and we find a new energy scale for the crossover to the ρ∝${\mathit{T}}^2$ behavior at low temperatures. This energy scale is finite even when the spin fluctuations are assumed to be critical. The effect of additional impurity scattering is discussed. For the model with Van Hove singularities, a standard ansatz for the Boltzmann equation is sufficient to show that although the quasiparticle lifetime is anomalously short, the resistivity ρ∝${\mathit{T}}^2$ ${\ln }^2$(1/T).