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We theoretically investigate electronic states and physical properties in atwo-channel Anderson lattice model to understand the non-Fermi liquid behaviorsobserved in PrV$_2$Al$_{20}$ and PrIr$_2$Zn$_{20}$ whose ground state of thecrystalline electric field for local $f$-electron is the $\Gamma_3$ non-Kramersdoublet of $f^2$-configuration and excited state is the $\Gamma_7$ Kramersdoublet of $f^1$-configuration. We use the expansion from the limit of largedegeneracy $N$ of the ground state ($1/N$-expansion), with $N$ being thespin-orbital degeneracy. Inclusion of the self-energy of the conductionelectrons up to the order of $O(1/N)$ leads to heavy electron with channel andspin-orbit degeneracies. We find that the electrical resistivity isproportional to temperature $T$ in the limit of $T\to0$ and follows$\sqrt{T}$-law in the wide region of temperature, i.e., $T_x<T<T_0$, wheretypical values of $T_x$ and $T_0$ are $T_x\sim10^{-3}T_{\rm K}$ and$T_0\sim10^{-2}T_{\rm K}$, respectively, $T_{\rm K}$ being the Kondotemperature of the model. We also find non-Fermi liquid behaviors at $T\llT_{\rm K}$ in a series of physical quantities; the chemical potential, thespecific heat, and the magnetic susceptibility, explaining the non-Fermi liquidbehaviors observed in PrV$_2$Al$_{20}$ and PrIr$_2$Zn$_{20}$. At the same time,we find that the Fermi liquid behavior becomes prominent for the system withsmaller hybridization between $f$- and conduction electrons, explaining theFermi liquid behaviors observed in PrTi$_2$Al$_{20}$.

Non-Fermi Liquid and Fermi Liquid in Two-Channel Anderson Lattice Model: Theory for Pr$A_2$Al$_{20}$ ($A$=V, Ti) and PrIr$_2$Zn$_{20}$