Universality in Heavy Fermion Systems with General Degeneracy

We discuss the relation between the $T^2$ coefficient of electrical resistivity $A$ and the $T$-linear specific-heat coefficient $\gamma$ for heavy-fermion systems with general $N$, where $N$ is the degeneracy of quasiparticles. A set of experimental data reveals that the Kadowaki-Woods relation, $A/{\gamma }^2=1\times {10}^{-5}\mu \Omega \mathrm{c}\mathrm{m}(\mathrm{K}\mathrm{m}\mathrm{o}\mathrm{l}/\mathrm{m}\mathrm{J}{)}^2$, collapses remarkably for large-$N$ systems, although this relation has been regarded to be commonly applicable to the Fermi liquids. Instead, based on the Fermi-liquid theory we propose a new relation, $\tilde{A}/{\tilde{\gamma }}^2=1\times {10}^{-5}$ with $\tilde{A}=A/\frac{1}{2}N(N-1)$ and $\tilde{\gamma }=\gamma /\frac{1}{2}N(N-1)$. This new relation exhibits an excellent agreement with the data for the whole range of degenerate heavy fermions.

Figure 1

$T^2$ coefficient of electrical resistivity $A$ vs $T$-linear coefficient of specific heat $\gamma$ of heavy-fermion systems with various degeneracy. Experimental data are taken from Refs. 7, 8, 9, 16, 17, 18. The black line corresponds to the Kadowaki-Woods relation [7]. Other solid lines are the prediction from the orbitally degenerate periodic-Anderson model [10]. Colors of the symbols represent the degeneracy $N$ probable for the systems: black, yellow, blue, and red indicate $N=2$, 4, 6, and 8, respectively. The value of $N$ of U compounds is not determined.

Figure 2

The plot of $\tilde{A}$ and $\tilde{\gamma }$ of heavy-fermion systems. $\tilde{A}$ and $\tilde{\gamma }$ are the divided values of $A$ and $\gamma$ by $\frac{1}{2}N(N-1)$, respectively. $N$ of the U-based compounds is tentatively assumed to be 2. The dotted line represents the grand-KW relation (4) given in the text: $\tilde{A}/{\tilde{\gamma }}^2=1\times {10}^{-5}\mu \Omega \mathrm{c}\mathrm{m}(\mathrm{K}\mathrm{m}\mathrm{o}\mathrm{l}/\mathrm{m}\mathrm{J}{)}^2$.