Electrical Conductivity of Fermi Liquids. II. Quasiparticle Transport

TL;DR

This paper develops a comprehensive theory of Fermi liquids to explain the universal Kadowaki-Woods relation, linking quasiparticle scattering and Fermi surface geometry, and demonstrates its applicability to heavy fermion compounds.

Contribution

It introduces a formula for the ratio of resistivity coefficient to specific heat squared, incorporating coupling and geometric factors, advancing understanding of strong coupling Fermi liquids.

Findings

The ratio A/γ^2 is expressed as a product of coupling and geometric parameters.

Universal ratio in heavy fermion compounds is explained by specific parameter values.

The theory suggests universal phenomena in strong coupling Fermi liquids.

Abstract

We develop a general theory of Fermi liquids to discuss the Kadowaki-Woods relation $A\propto \gamma^2$. We derive a formula for the ratio $A/\gamma^2$ which is expressed as a product of two dimensionless parameters $\alpha$ and $F$, where $\alpha$ represents a coupling constant for quasiparticle scattering and $F$ is a geometric factor determined by the shape of the Fermi surface. Then we argue that the universal ratio observed in heavy fermion compounds is reproduced under the conditions $\alpha\sim 1$ and $F\sim 20$. The former is regarded as a universality of Fermi liquids in a strong coupling regime, and the latter is corroborated by evaluating $F$ definitely in simple cases. It is noted that the proportional relation is just an example of the universal phenomena to be expected for the whole class of strong coupling Fermi liquids.