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

Abstract

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, $A=ρ(T)/T^2$, 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.