Frequency Dependent Transport in Heavy Fermion Systems.

The unusual properties found in heavy fermion compounds have recently attracted a great deal of interest in both the experimental and theoretical communities. Various thermodynamic quantities such as the electronic specific heat and the magnetic susceptibility are extremely large at low temperatures, and narrow features in the density of states around the Fermi energy resulting from strong electron correlations are usually associated with this enhanced behavior. Fermi liquid theory leads to the notion of an enhanced relaxation time and mass which are observable in the frequency dependent response. Measurements of the electrical conductivity in the millimeter wave spectral range (35 GHz to 150 GHz) are reported in this manuscript for CePd_3 , UPt_3, CeAl_3 , and UBe_{13}. Using resonant cavities, the surface resistance R_ {rm s} was determined from the change in the quality factor in the temperature interval from 300 K to 1.2 K. Assuming the imaginary component of the response is negligible, the real conductivity was extracted from R_{rm s}. The frequency dependence of the low temperature data was analyzed in terms of a Drude theory incorporating a renormalized relaxation time tau* and m*. Our findings qualitatively agree with this type of expression supporting the conjectures of Varma and Fukuyama, and the theoretical models advanced by Millis, Lee, and Coleman. In all the compounds studied, long relaxation times around 10^{-12}s are encountered. Combining tau* with the d.c. conductivity yields a renormalized plasma frequency omega _sp{rm p}{*} characterizing the strong correlations. Two alternative strategies are available for computing the mass enhancement. One possibility is to compare omega_sp{rm p}{*} with the unrenormalized plasma frequency omega_{rm p} measured in optical experiments. From this procedure, a mass enhancement relative to the band mass is calculated. The second method involves combining omega_sp {rm p}{*} and the specific heat coefficient gamma to arrive at an enhancement factor with respect to the free electron mass. In either case, the enhancements range from 10 to 1000 in the four materials. A comparison between the various systems is given along with a discussion of the uncertainties in the analysis.