Multiple temperature scales of the periodic Anderson model: Slave boson approach

Abstract

The thermodynamic and transport properties of intermetallic compounds with Ce, Eu, and Yb ions are discussed using the periodic Anderson model with an infinite correlation between f electrons. At high temperatures, these systems exhibit typical features that can be understood in terms of a single impurity Anderson or Kondo model with Kondo scale TK . At low temperatures, the normal state is governed by the Fermi liquid (FL) laws with characteristic energy scale T0. The slave boson solution of the periodic model shows that T0 and TK depend not only on the degeneracy and the splitting of the f states, the number of c and f electrons, and their coupling, but also on the shape of the conduction electrons density of states (c DOS) in the vicinity of the chemical potential.We show that the details of the band structure determine the ratio T0/TK and that the crossover between the high-and low-temperature regimes in ordered compounds is system-dependent. A sharp peak in the c DOS yields T0 ≪TK and explains the 'slow crossover' observed in YbAl3 or YbMgCu4. A minimum in the c DOS yields T0 ≫TK , which leads to the abrupt transition between the high-and low-temperature regimes in YbInCu4. In the case of CeCu2Ge2 and CeCu2Si2, where T0 ≃ TK , the slave boson solution explains the pressure experiments which reveal sharp peaks in the T 2 coefficient of the electrical resistance, A = ρ(T )/T 2 , and the residual resistance. These peaks are due to the change in the degeneracy of the f states induced by the applied pressure.The FL laws explain also the correlation between the specific heat coefficient γ = CV /T and the slope of the thermopower α(T )/T , or between γ and the A coefficient of the resistivity. For N -fold degenerate model, the FL laws explain the deviations from universal value of the Kadowaki-Woods ratio, RKW = A/γ 2 , and the ratio q = lim {T →0} α/γT . The renormalization of transport coefficients can invalidate the Wiedemann-Franz law and lead to an enhancement of the thermoelectric figure-ofmerit. We show that the low-temperature response of the periodic Anderson model can be enhanced (or reduced) with respect to the predictions based on the single-impurity models that give the same high-temperature behavior.

Low Energy Scales of Kondo Lattices: Mean-field Perspective

“…[4,21]. The exponential factor in both T 0 and T K , results in a very sensitive dependence of these energy scales with respect to small changes in the system (e.g., pressure or doping).…”

“…Since the ratio T 0 /T K does not depend on J K , it is more likely to be analyzed experimentally as a universal function. The mean-field solution yields [4] …”

“…The coherence temperature, T 0 , results from the Kondo effect, but, unlike T K , characterizes a Fermi liquid with a large Fermi surface. Here we consider the effects due to the shape variation of the non-interacting DOS, ρ 0 (ω) [4]. In order to separate this effect from the electronic filling effects, we assume that n c is close to 1, but not exactly half full, so that the system is metallic.…”

“…The Fermi-liquid regime is characterized by an energy scale, T 0 , which can be defined identically from different physical properties of the ground state: the quasiparticle density of states, ρ = 1/T 0 , the Sommerfeld coefficient, Γ = lim T →0 C V (T )/T = 1/T 0 , or the local impurity spin susceptibility, χ loc (T = 0) = 1/T 0 . We have obtained explicit expressions for T K and T 0 in the limit of small J K [4,21]:…”

“…2 is generalized [4], resulting in an effective Hamiltonian formally similar to Eq. (2), with spin-dependent f −fermion potentials, λ → λ + σ h. The effective hybridization, r, remains spin-independent.…”