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${}_{20}$

Abstract

We theoretically investigate electronic states and physical properties in a two-channel Anderson lattice model to understand the non-Fermi liquid behaviors observed in PrV${}_2$Al${}_{20}$ and PrIr${}_2$Zn${}_{20}$ whose ground state of the crystalline electric field for local $f$-electron is the ${\Gamma }_3$ non-Kramers doublet of $f^2$-configuration and excited state is the ${\Gamma }_7$ Kramers doublet of $f^1$-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 $T\to 0$ and follows $\sqrt{T}$-law in the wide region of temperature, i.e., $T_x<T<T_0$, where typical values of $T_x$ and $T_0$ are $T_x\sim 10^{-3}{T}_{\mathrm{K}}$ and $T_0\sim 10^{-2}{T}_{\mathrm{K}}$, respectively, $T_{\mathrm{K}}$ being the Kondo temperature of the model. We also find non-Fermi liquid behaviors at $T\ll T_{\mathrm{K}}$ in a series of physical quantities; the chemical potential, the specific heat, and the magnetic susceptibility, explaining the non-Fermi liquid behaviors observed in 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 with smaller hybridization between $f$- and conduction electrons, explaining the Fermi liquid behaviors observed in PrTi${}_2$Al${}_{20}$.

37 pages, 17 figures

References in corpus (4)

• Signatures of valence fluctuations in CeCu2Si2 under high pressure
• Resolution of Entropy $\ln \sqrt{2}$ by Ordering in Two-Channel Kondo Lattice
• Crystalline-Electric-Field Effect on the Resistivity of Ce-based Heavy Fermion Systems
• Competition between Quadrupole and Magnetic Kondo Effects in Non-Kramers Doublet Systems

Cited by in corpus (22)

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• Unveiling Hidden Orders: Magnetostriction as a Probe of Multipolar-Ordered States
• Single-Site Non-Fermi Liquid Behaviors in a Diluted 4$f^2$ System Y${}_{1-x}$Pr${}_x$Ir${}_2$Zn${}_{20}$
• NMR Observation of Ferro-quadrupole Order in PrTi2Al20
• Anisotropic B-T Phase Diagram of Non-Kramers System PrRh2Zn20
• Classical Monte Carlo study for antiferro quadrupole orders in a diamond lattice
• Two-channel Kondo Effect Emerging from Nd Ions
• Field-Induced Switching of Ferro-Quadrupole Order Parameter in PrTi2Al20
• Channel-selective non-Fermi liquid behavior in the two-channel Kondo lattice model under a magnetic field
• Field-induced Ferrohastatic Order in Cubic Non-Kramers Doublet Systems
• Triple-$q$ quadrupole-octupole order scenario for PrV${}_2$Al${}_{20}$
• Competing Kondo Effects in Non-Kramers Doublet Systems
• Unveiling Quadrupolar Kondo Effect in the Heavy Fermion Superconductor PrV${}_2$Al${}_{20}$
• Hindered Quadrupole Order in PrMgNi4 with a Nonmagnetic Doublet Ground State
• Non-Fermi liquid behavior and quantum criticality in cubic heavy fermion systems with non-Kramers multipolar local moments
• Unconventional Non-Fermi Liquid Properties of Two-Channel Anderson Impurities System
• Simultaneous collapse of antiferroquadrupolar order and superconductivity in PrIr${}_2$Zn${}_{20}$ by nonhydrostatic pressure
• Inelastic neutron scattering study of crystalline electric field excitations in the caged compounds NdT2Zn20 (T = Co, Rh, and Ir)
• Strange-metal behavior without fine-tuning in PrV2Al20
• Elastic Response in the Dilute non-Kramers System Y${}_{1-x}$Pr${}_x$Ir${}_2$Zn${}_{20}$
• Numerical Renormalization Group Study of Quadrupole Kondo Effect with the Crystal-field Excited State