Kondo regime

In mesoscopic physics, because the geometries can be controlled so well, and because the measurements are very accurate, current under different conditions can be appropriately measured and calculated. The models used for mesoscopic transport are the so-called Landauer/Imry/Buttiker elastic scattering model for current, correlated electronic structure schemes to deal with Coulomb blockade limit and Kondo regime transport, and charging algorithms to characterize the effects of electron populations on the quantum dots. These are often based on capacitance analyses (this is a matter of thinking style - most chemists do not consider capacitances when discussing molecular transport junctions). 

An alternative approach to accounting for the maxima in the temperature dependence of p is based on the Kondo-lattice model (Lavagna et al. 1982). The periodic array of independent Kondo impurities, described by the single-ion Kondo temperature TK, provides a proper description at elevated temperatures, while a coherent state yielding a drop of the resistivity is attained when the system is cooled to below another characteristic temperature coh- Although this approach is suitable particularly for Ce compounds where the Kondo regime was identified inequiv-ocally, the coherence effects are probably significant also in narrow-band actinide materials, as indicated by an extreme sensitivity of the lower-temperature decrease of the resistivity to the presence of impurities. 

Fig. 3.30. Phase diagram of the U(Pt1 Pd l)3 system. Tc ( ) and TN (o) as a function of Pd concentration up to 10 at.% of Pd. S indicates the superconducting phase, AF the antiferromagnetic phase, K the Kondo regime, and SF the spin-fluctuation region which persists into the AF region. The arrows indicate the sign of the increasing pressure effect on C> 7sF> and 7V Note the expanded scale for Pd concentrations below 0.5 at.% (Franse et al. 1987a).

From Coleman 1984.) Inset shows the temperature variation of the normalized Kondo resonance weight Sn (T) = SnXT)/Sn/0). This is a universal function of T/T , independent of model parameters in the Kondo regime. (From Cox 1985.)... 

Fig. 7. The two sequences of pictures show the growth of correlations with increasing Coulomb parameter U in the Kondo regime Cj = -3A of an Anderson impurity (a) and a lattice (b). The characteristic temperatures and T, respectively, that vary with U and are largest for the impurity with U = 16 [last picture in (a)], i.e., k Ty O.OfZA, exceed in all cases the temperature k T = 0.024 chosen. For the lattice, the band DOS (dark dashed) is shown in addition to the DOS of the localized electrons. Both curves exhibit simultaneous formation of the coherence gap with decreasing temperature. A comparison with the Hartree-Fock solution of the model (broken curves) gives an estimate of the many-body nature of ail the features, which is small for t/ < 4 and very essential for large U > A. Units as in fig. 4.

Fig. 27. Resistivity p(T) (a), thermoelectric power S(T) and Lorenz number L T) (b), calculated with LNCA techniques for a sixfold degenerate Anderson lattice model in the Kondo regime (Cox and Grewe 1988). Impurity results, scaled with concentration are shown for comparison. The resistivity results exhibit the logarithmic increase with decreasing temperature and the coherence-derived decrease below T = to the residual value due to impurities, which is quadratic in the Fermi liquid regime T < T. S(T ) is positive definite for the simple model situation chosen.

Contrary to what happens at large U, higher V tends to enhance the hybridization of 4f electrons with conduction electrons, thus accelerating the delocalization of the 4f electrons (Koelling et al. 1985). The delocalization of 4f electrons tends to make the 4f band wide. When Ef > V, we have still better localization and expect the Kondo regime in the Ce (or Yb) compounds. 

There is a big difference in f-electron character between the Kondo regime and the valence-fluctuation regime. One may be tempted to think that the 4f electrons in a Kondo lattice compound with a large value of Tk are itinerant. This seems to be true, as shown later in detail for CeSns and CeNi or CeRu2Si2. 

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