Optical Spectroscopy of anomalous Fermi Liquids.

It is customary to classify a metallic conductor as a Fermi liquid if, at low temperatures, the electrical resistivity varies as the square of the absolute temperature. Fermi liquid theory shows that if umklapp scattering dominates then, independent of a particular band structure, this T squared dependence is accompanied by a quadratic frequency dependence where $\rho ({\rm T},\omega )=C(\omega^{2\thinspace }+b(\pi {\rm T})^{2})$ where the scaling constant $b=$4 for a Fermi liquid[1,2]. A survey of literature shows that where spectroscopic data exist$, b=$4 has not been generally observed[3]. We find that, surveying the recent literature, that in heavy fermion systems the scaling coefficient $b=$1, pointing to a resonant scattering mechanism [2]. In most other systems an unknown mechanism yields a value of $b$ of around 2. 1. R. N. Gurzhi, Sov. Phys. JETP \textbf{14}, 886 (1962). 2. D.L. Maslov and A.V. Chubukov, Phys. Rev. B \textbf{86}, 155137 (2012). 3. U. Nagel \textit{et al}. PNAS \textbf{109}, 19161 (2012).