Electronic State and Magnetic Susceptibility in Orbitally Degenerate (J=5/2) Periodic Anderson Model

Kontani, Hiroshi; Yamada, Kōsaku

doi:10.1143/jpsj.66.2232

Cited by 17 publications

(19 citation statements)

References 17 publications

(32 reference statements)

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“…When N f is larger than the number of conduction band N c , almost unhybridized f -levels exist near the Fermi level, except when the crystal-field splitting is very large. This situation induces a huge anomalous Hall coefficient [277] as well as the large Van Vleck susceptibilities [303,304] in Kondo insulators and in singlet SC heavy-fermion systems.…”

Section: Fermi Arc Picture and Transport Phenomenamentioning

confidence: 99%

Anomalous transport phenomena in Fermi liquids with strong magnetic fluctuations

Kontani¹

2008

Rep. Prog. Phys.

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In this paper, we present a recent developments in the theory of transport phenomena based on the Fermi liquid theory. In conventional metals, various transport coefficients are scaled according to the quasiparticles relaxation time, τ , which implies that the relaxation time approximation (RTA) holds well. However, such a simple scaling does not hold in many strongly correlated electron systems. The most famous example would be high-T c superconductors (HTSCs), where almost all the transport coefficients exhibit a significant deviation from the RTA results. This issue has been one of the most significant unresolved problems in HTSCs for a long time. Similar anomalous transport phenomena have been observed in metals near their antiferromagnetic (AF) quantum critical point (QCP). The main goal of this study is to demonstrate whether the anomalous transport phenomena in HTSC is the evidence of non-Fermi liquid ground state, or it is just the RTA violation in strongly correlated Fermi liquids. Another goal is to establish a unified theory of anomalous transport phenomena in metals with strong magnetic fluctuations. For these purposes, we develop a method for calculating various transport coefficients beyond the RTA by employing field theoretical techniques.In a Fermi liquid, an excited quasiparticle induces other excited quasiparticles by collision, and current due to these excitations is called a current vertex correction (CVC). Landau had noticed the existence of CVC first, which is indispensable for calculating transport coefficient in accord with the conservation laws. Here, we develop a transport theory involving resistivity and Hall coefficient on the basis of the microscopic Fermi liquid theory, by considering the CVC. In nearly AF Fermi liquids, we find that the strong backward scattering due to AF fluctuations induces the CVC with prominent momentum dependence. This feature of the CVC can account for the significant enhancements in the Hall coefficient, magnetoresistance, thermoelectric power, and Nernst coefficient in nearly AF metals. According to the present numerical study, aspects of anomalous transport phenomena in HTSC are explained in a unified way by considering the CVC, without introducing any fitting parameters; this strongly supports the idea that HTSCs are Fermi liquids with strong AF fluctuations. Further, the present theory also explains very similar anomalous transport phenomena occurring in CeM In 5 (M =Co or Rh), which is a heavy-fermion system near the AF QCP, and in the organic superconductor κ-(BEDT-TTF).In addition, the striking ω-dependence of the AC Hall coefficient and the remarkable effects of impurities on the transport coefficients in HTSCs appear to fit naturally into the present theory. Many aspects of the present theory are in accord with the anomalous transport phenomena in HTSCs, organic superconductors, and heavyfermion systems near their AF QCPs. We discuss some of the open questions for future work.

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Section: Fermi Arc Picture and Transport Phenomenamentioning

confidence: 99%

Anomalous transport phenomena in Fermi liquids with strong magnetic fluctuations

Kontani¹

2008

Rep. Prog. Phys.

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166

233

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“…We expect this intrinsic AHE is widely observed since the J =5/2 PAM is a well-established effective model for Ce-based HF systems: For example, it could explain a large Van-Vleck susceptibility in the Kondo insulator. 47,48 There remains a lot of work to be done on the AHE in HF systems. For example, Nakajima et al found that the AHC in the two-dimensional HF system CeMIn 5 ͑M =Co,Rh,Ir͒ is negligibly small.…”

Section: Comparison With Experiments: Heavy Fermionsmentioning

confidence: 99%

Intrinsic anomalous Hall effect in ferromagnetic metals studied by the multi-d-orbital tight-binding model

2007

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To elucidate the origin of anomalous Hall effect ͑AHE͒ in ferromagnetic transition metals, we study the intrinsic AHE based on a multiorbital ͑d xz , d yz ͒ tight-binding model. We find that a large anomalous velocity comes from the off-diagonal ͑interorbital͒ hopping. For this reason, the present model shows a large intrinsic anomalous Hall conductivity ͑AHC͒ which is compatible with typical experimental values in ferromagnets ͑10 2 -10 3 ⍀ −1 cm −1 ͒, without the necessity to assume a special band structure at the Fermi level. In good metals where is small, the intrinsic AHC is constant ͑dissipationless͒ as found by Karplus and Luttinger. In bad metals, however, we find that the AHC is proportional to −2 when ប /2 is larger than the minimum band splitting measured from the Fermi level ⌬. This crossover behavior of the intrinsic AHE, which was derived in J. Phys. Soc. Jpn. 63, 2627 ͑1994͒, was recently observed in various ferromagnetic metals universally by Asamitsu et al. We also stress that the present ͑d xz , d yz ͒ tight-binding model shows a huge spin Hall effect in a paramagnetic state.

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“…In the next stage, we study the KW relation in the weak coupling region (1/z > ∼ 1) using the second-orderperturbation-approximation (SOPA) with respect to U , both for J = 1/2 case and J = 7/2 case [17]. In the numerical calculation, we use the spherical Brillouin zone (|k| ≤ π) for simplicity of the numerical calculation.…”

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“…We note again that E f > µ in the present calculation by considering the particle-hole transformation for 4f 13 -electrons in Yb 3+ (J=7/2). In the case of U = 2, the DOS around the Fermi level and E f level are renormalized within a smaller energy width due to the ǫ-dependence of ReΣ(ǫ) [17,20].…”

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confidence: 99%

Generalized Kadowaki–Woods Relation in Heavy Fermion Systems with Orbital Degeneracy

Kontani

2004

J. Phys. Soc. Jpn.

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We present a theoretical study of the Kadowaki-Woods relation in the orbitally degenerate periodic Anderson model. Based on Fermi liquid theory, we derive the generalized Kadowaki-Woods relation in the strong coupling limit, Aγ −2 ≈ 10 −5 / . Thus, the KW relation has been considered as one of the remarkably robust signature of Fermi liquids, irrespective of the value of m * . It can be derived microscopically using the FL theory [3], or using the slave-boson method [4]. Note that the KW relation holds experimentally even in the close vicinity of a magnetic quantum critical point under a magnetic field [5], the fact of which is consistent with theoretical analyses [6][7][8].Recently [µΩcm(mol·K/mJ) 2 ], which is consistent with experimental observations. This is the first theoretical derivation of the KW relation in orbitally degenerate systems.As discussed in ref.[2], the violation of the KW relation in Yb-compounds cannot be ascribed to the impurity effect nor an accidental singularity of the band structure inherent to individual compounds. For this reason, we attack this universal issue based on a conventional orbitally degenerate periodic Anderson model (OD-PAM) with a single conduction band. Because of the strong L-S coupling, the f -electron state for Yb 3+ -ion with 4f 13(Ce +3 -ion with 4f 1 ) is specified by the total angular momentum J = 7/2 (J = 5/2) and its z-component M . The degeneracy of f -orbital is N = 2J + 1.Here, we study the following OD-PAM [15][16][17]:

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Electronic State and Magnetic Susceptibility in Orbitally Degenerate (J=5/2) Periodic Anderson Model

Cited by 17 publications

References 17 publications

Anomalous transport phenomena in Fermi liquids with strong magnetic fluctuations

Anomalous transport phenomena in Fermi liquids with strong magnetic fluctuations

Intrinsic anomalous Hall effect in ferromagnetic metals studied by the multi-d-orbital tight-binding model

Generalized Kadowaki–Woods Relation in Heavy Fermion Systems with Orbital Degeneracy

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