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

TL;DR

This paper investigates how resistivity varies with temperature in models relevant to high-temperature superconductors, revealing new energy scales and behaviors through advanced variational solutions and Boltzmann equation analysis.

Contribution

It introduces an improved variational approach for calculating resistivity and identifies a finite energy scale for the crossover to quadratic temperature dependence.

Findings

Resistivity shows a crossover to $ ho \\propto T^2$ at a finite energy scale.

In models with van Hove singularities, resistivity behaves as $T^2 \\ln(1/T)$ despite short quasiparticle lifetimes.

Impurity scattering effects are discussed in the context of resistivity behavior.

Abstract

We calculate the resistivity $\rho$ 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 semiclassicaly 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 $\rho\propto T^2$ 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 $\rho\propto T^2\ln(1/T)$.