Relaxation-time enhancement in the heavy-fermion systemsCePd3andUPt3

The frequency dependence of the electrical conductivity was measured at microwave- and millimeter-wave frequencies in the heavy-fermion materials ${\mathrm{CePd}}_3$ and ${\mathrm{UPt}}_3$. Although the conductivity is independent of the frequency at high temperatures, a substantial deviation from the dc conductivity develops in the low-temperature, ‘‘coherent’’ regime. The observed dependence on frequency agrees with a Drude expression ${\mathrm{\sigma }}_1$(ω)=${\mathrm{\sigma }}_{\mathit{dc}}$/(1+${\mathrm{\omega }}^2$ ${\mathrm{\tau }}^{\mathrm{*}2}$), incorporating a renormalized relaxation time ${\tau }^{\mathrm{*}}$ typically around ${10}^{\mathrm{-}12}$ s. From ${\tau }^{\mathrm{*}}$ and the measured ${\sigma }_{\mathrm{dc}}$, the renormalized plasma frequency, ${\mathrm{\omega }}_{\mathit{p}}^{\mathrm{*}}$=(${\mathrm{\sigma }}_{\mathit{dc}}$/${\mathrm{\epsilon }}_0$ ${\mathrm{\tau }}^{\mathrm{*}}$ ${)}^{1/2}$ is evaluated. By comparison of ${\omega }_p^{\mathrm{*}}$ with the plasma frequency obtained at optical frequencies, where renormalization effects do not occur, an enhanced mass is extracted. Similar results are found by comparison of ${\omega }_p^{\mathrm{*}}$ with the linear specific-heat coefficient. The enhanced relaxation time is approximately given by the expression ${\tau }^{\mathrm{*}}$/τ=$m^{\mathrm{*}}$/$m_e$, where τ and $m_e$ refer to the unrenormalized quantities, supporting the conjectures of Varma and Fukuyama, and the theoretical models advanced by Millis and co-workers, Auerbach and co-workers, and Coleman. An internally consistent analysis of σ(ω) in terms of an enhanced relaxation time also suggests that a frequency-dependent density of states does not play a dominant role in the frequency-dependent response measured in the millimeter-wave spectral range. Possible Fermi-liquid and low-energy density-of-state contributions to the frequency-dependent conductivity are also discussed.