Multiple temperature scales of the periodic Anderson model: the slave bosons approach

The thermodynamic and transport properties of intermetallic compounds with Ce, Eu, and Yb ions are discussed using the periodic Anderson model with an infinite correlation between $f$ electrons. The slave boson solution of the periodic model shows that the Fermi liquid scale T$_0$ and the Kondo scale T$_K$ depend on the shape of the conduction electrons density of states ($c$ DOS) in the vicinity of the chemical potential, that the details of the band structure determine the ratio T$_0$/T$_K$, and that the crossover between the high- and low-temperature regimes in ordered compounds is system-dependent. A sharp peak in the $c$ DOS yields T$_0 \ll$T$_K$ and explains the 'slow crossover' observed in YbAl$_3$ or YbMgCu$_4$. A minimum in the $c$ DOS yields T$_0 \gg$T$_K$, which leads to the abrupt transition between the high- and low-temperature regimes in YbInCu$_4$. In the case of CeCu$_2$Ge$_2$ and CeCu$_2$Si$_2$, where T$_0 \simeq T_K$, the slave boson solution explains the pressure experiments which reveal sharp peaks in the T$^2$ coefficient of the electrical resistance, $A=\rho(T)/T^2$, and the residual resistance. These peaks are due to the change in the degeneracy of the $f$ states induced by the applied pressure. We show that the low-temperature response of the periodic Anderson model can be enhanced (or reduced) with respect to the predictions based on the single-impurity models that give the same high-temperature behavior.