Relaxation-time enhancement in the heavy-fermion systems CePd3 and UPt3.

Abstract

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 ${\mathrm{\ensuremath{\sigma}}}_{1}$(\ensuremath{\omega})=${\mathrm{\ensuremath{\sigma}}}_{\mathit{dc}}$/(1+${\mathrm{\ensuremath{\omega}}}^{2}$${\mathrm{\ensuremath{\tau}}}^{\mathrm{*}2}$), incorporating a renormalized relaxation time ${\ensuremath{\tau}}^{\mathrm{*}}$ typically around ${10}^{\mathrm{\ensuremath{-}}12}$ s. From ${\ensuremath{\tau}}^{\mathrm{*}}$ and the measured ${\ensuremath{\sigma}}_{\mathrm{dc}}$, the renormalized plasma frequency, ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}^{\mathrm{*}}$=(${\mathrm{\ensuremath{\sigma}}}_{\mathit{dc}}$/${\mathrm{\ensuremath{\epsilon}}}_{0}$${\mathrm{\ensuremath{\tau}}}^{\mathrm{*}}$${)}^{1/2}$ is evaluated. By comparison of ${\ensuremath{\omega}}_{p}^{\mathrm{*}}$ 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 ${\ensuremath{\omega}}_{p}^{\mathrm{*}}$ with the linear specific-heat coefficient. The enhanced relaxation time is approximately given by the expression ${\ensuremath{\tau}}^{\mathrm{*}}$/\ensuremath{\tau}=${m}^{\mathrm{*}}$/${m}_{e}$, where \ensuremath{\tau} 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 \ensuremath{\sigma}(\ensuremath{\omega}) 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.