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Pré-Publication, Document De Travail Année : 2002

Kondo effect in " bad metals "

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We study the low-temperature properties of a Kondo lattice using the large−N formalism. For a singular density of conduction states (DOS), we generalize the single-impurity result of Withoff and Fradkin: the strong-coupling fixed point becomes irrelevant if the DOS vanishes at the Fermi level EF. However, for EF close enough to the singularity, and close to half-filling, the Kondo temperature, TK , can become much smaller than the characteristic Fermi liquid scale. At T=0, a meta-magnetic transition occurs at the critical magnetic field Hc ≃ (kB/µB)TK. Our results provide a qualitative explanation for the behavior of the YbInCu4 compound below the valence-change transition. The Kondo model has been introduced to explain the transport and thermodynamic anomalies of dilute magnetic alloys [1] due to weak interaction between the conduction electrons and impurity spins. The model is defined by the Hamiltonian H K = Js · S, where s and S are the spins of conduction and localized electrons, respectively , and J is the coupling constant. Our current understanding of Kondo systems is based on the solutions obtained by the peturbative scaling [2], numerical renor-malization group [3], and Bethe Ansatz [4], which are usually derived for a featureless conduction band. The main result is the crossover from the high-temperature regime, where the impurity is magnetic and the conduction electrons are only weakly perturbed by the spins, to the strong coupling regime, where the magnetic moment is screened completely and the conduction states form a Fermi liquid [3]. The Kondo temperature separates these two regimes and is the only relevant energy scale. Kondo systems with a non-constant DOS or a high concentration of magnetic impurities show more complicated behavior. Assuming an electron-hole symmetry and a DOS with a power-law singularity at the Fermi level E F , Whithoff and Fradkin [5] found a critical coupling J c such that for J > J c the dilute Kondo systems scale to the strong coupling limit, while for J < J c the renormal-ized coupling decreases with temperature and the " usual " Kondo screening does not occur. Here, we study the low-temperature Kondo effect in bad metals and consider a lattice of magnetic ions coupled by exchange interaction to a conduction band with a minimum (or a gap or a pseudo-gap) close to E F. We show that such a model generates more than one energy scale and explains the low-temperature behavior of Yb-and Eu-based intermetal-lic compounds, like YbInCu 4 [6], EuNi 2 (Si 1−x Ge x) 2 [7] or Eu(Pd 1−x Pt x) 2 Si 2 [8], which exhibit a valence-change transition. We also study the Kondo lattice with an enhanced DOS around E F and show that it explains the properties of YbAl 3 [9] in the coherent regime. The Kondo lattice Hamiltonian reads, H =
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hal-01556194 , version 1 (04-07-2017)

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Sébastien Burdin, V Zlati´c. Kondo effect in " bad metals ". 2002. ⟨hal-01556194⟩
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