Generalized Kadowaki-Woods Relation in Heavy Fermion Systems with Orbital Degeneracy

TL;DR

This paper derives a generalized Kadowaki-Woods relation for orbitally degenerate heavy fermion systems using Fermi liquid theory, explaining smaller observed ratios in Yb-based compounds.

Contribution

It introduces a new generalized relation linking resistivity and specific heat in orbitally degenerate systems, extending the classic Kadowaki-Woods relation.

Findings

Derived the generalized relation $A\gamma^{-2} \\approx 10^{-5} N(N-1)/2$

Explains smaller $A\gamma^{-2}$ values in Yb-based heavy fermion systems

Provides theoretical support for experimental observations

Abstract

We present a theoretical study of the Kadowaki-Woods relation in the orbitally degenerate periodic Anderson model. Based on Fermi liquid theory, we derive the generalized Kadowaki-Woods relation in the strong coupling limit, $A\gamma^{-2} \approx 10^{-5} N(N-1)/2$ [\mu\Omega cm(mol K/mJ)^2], where $A$ is the coefficient of the $T^2$ term in the resistivity, $\gamma$ is the $T$-linear specific heat coefficient, and $N$ is the $f$-orbital degeneracy. This result naturally explains the remarkably smaller value of $A\gamma^{-2}$ in various orbitally degenerate (mainly Yb-based) heavy Fermion systems, reported by Tsujii et al.: J. Phys. Cond. Mat. 15 (2003) 1993.