Kondo effect in the seven-orbital Anderson model hybridized with Γ8 conduction electrons

Abstract

We clarify the two-channel Kondo effect in the seven-orbital Anderson model hybridized with Γ 8 conduction electrons by employing a numerical renormalization group method. From the numerical analysis for the case with two local f electrons, corresponding to Pr 3+ or U 4+ ion, we confirm that a residual entropy of 0.5 log 2, a characteristic of two-channel Kondo phenomena, appears for the local Γ 3 non-Kramers doublet state. For further understanding on the Γ 3 state, the effective model is constructed on the basis of a j-j coupling scheme. Then, we rediscover the two-channel s-d model concerning quadrupole degrees of freedom. Finally, we briefly introduce our recent result on the two-channel Kondo effect for the case with three local f electrons.

Two-Channel Kondo Effect Emerging from Np and Pu Ions

“…When we accommodate two holes into this situation, we easily obtain Γ 1 singlet and Γ 5 triplet for B 0 4 < 0 and B 0 4 > 0, respectively, by standard positive Hund's rule coupling. Note that the results are just reversed in comparison with the the case of n = 2, in which we have found Γ 1 singlet and Γ 5 triplet for B 0 4 > 0 and B 0 4 < 0, respectively [12], since the signs in the one-electron potentials are changed between the electron and hole pictures. As for Γ 3 doublet, it appears for B 0 6 > 0 near the region of B 0 4 ≈ 0.…”

“…On the basis of our belief, we have examined the Kondo effect for the case of plural numbers of f electrons in rareearth and actinide compounds by analyzing a seven-orbital impurity Anderson model hybridized with Γ 8 conduction bands with the use of a numerical renormalization group (NRG) method [11]. First we have reconfirmed the appearance of quadrupole two-channel Kondo effect for the case of n = 2 [12], where n denotes the local f electron number per ion. Then, we have moved onto the case of n = 3, corresponding to Nd ion, in which we have clarified the emergence of magnetic two-channel Kondo effect for the case with a Γ 6 ground state [13].…”

Microscopic Theory of Γ3 Quadrupole Ordering in Pr Compounds on the Basis of a j–j Coupling Scheme

“…Then, two-channel Kondo effects was found not only in the Pr ion but also in Nd and other rare-earth systems in an unbiased manner. 31,32) Concerning the multipole ordering, the seven-orbital Hubbard model has also been analyzed with the use of the RPA for the evaluation of multipole susceptibility. Such calculations have actually been performed, 15) but it was difficult to clarify the mechanism of the multipole ordering from a microscopic viewpoint, mainly due to the complexity originating from the large number of orbitals.…”

Yu-Shiba-Rusinov states of a single magnetic molecule in ans-wave superconductor

“…Theoretically, the emergence of in-gap bound states was predicted by Yu [18], Shiba [19], and Rusinov [20] using semiclassical approaches where, specifically, the spin moment was treated as classical. Quantum effects of magnetic impurities were later studied within mean-field theory [21][22][23], perturbation theory [24,25], and numerical renormalization group (NRG) theory [26][27][28][29][30][31].…”