Non-Fermi Liquid and Fermi Liquid in Two-Channel Anderson Lattice Model: Theory for PrA₂Al₂₀ (A=V, Ti) and PrIr₂Zn₂₀

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We theoretically investigate electronic states and physical properties in a two-channel Anderson lattice model to understand the non-Fermi liquid behaviors observed in PrV₂Al₂₀ and PrIr₂Zn₂₀ whose ground state of the crystalline electric field for local f-electron is the Γ₃ non-Kramers doublet of f²-configuration and excited state is the Γ₇ Kramers doublet of f¹-configuration. We use the expansion from the limit of large degeneracy N of the ground state (1/N-expansion), with N being the spin-orbital degeneracy. Inclusion of the self-energy of the conduction electrons up to the order of O(1/N) leads to heavy electron with channel and spin-orbit degeneracies. We find that the electrical resistivity is proportional to temperature T in the limit of T→0 and follows √T-law in the wide region of temperature, i.e., Tₓ<T<T₀, where typical values of Tₓ and T₀ are Tₓ 10⁻³T K and T₀ 10⁻²T K, respectively, T K being the Kondo temperature of the model. We also find non-Fermi liquid behaviors at T≪ T K in a series of physical quantities; the chemical potential, the specific heat, and the magnetic susceptibility, explaining the non-Fermi liquid behaviors observed in PrV₂Al₂₀ and PrIr₂Zn₂₀. At the same time, we find that the Fermi liquid behavior becomes prominent for the system with smaller hybridization between f- and conduction electrons, explaining the Fermi liquid behaviors observed in PrTi₂Al₂₀.