Kondo-hole substitution in heavy fermions: dynamics and transport

Kondo-hole substitution is a unique probe for exploring the interplay of interactions, f-electron dilution and disorder in heavy fermion materials. Within the diluted periodic Anderson model, we investigate the changes in single-particle dynamics as well as response functions, as a function of Kondo hole concentration ($x$) and temperature. We show that the spectral weight transfers due to Kondo hole substitution has characteristics that are different from those induced by temperature; The dc resistivity crosses over from a highly non-monotonic form with a coherence peak in the $x\rightarrow 0$ limit to a monotonic single-impurity like form that saturates at low temperature. The thermopower exhibits a characteristic maximum as a function of temperature, the value of which changes sign with increasing $x$, and its location is shown to correspond to a low energy scale of the system. The Hall coefficient also changes sign with increasing $x$ at zero temperature and is highly temperature dependent for all $x$. As $x$ is increased beyond a certain $x_c$, the Drude peak and the mid-infrared peak in the optical conductivity vanish almost completely; A peak in the optical scattering rate melts and disappears eventually. We discuss the above-mentioned changes in the properties in terms of a crossover from coherent, Kondo lattice behaviour to single impurity like, incoherent behaviour with increasing $x$. A comparison of theory with experiments carried out for the dc resistivity and the thermopower of Ce$_{1-x}$La$_x$B$_6$ yields good agreement.