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It is shown that the large-N approach yields two energy scales for the Kondo lattice model. The single-impurity Kondo temperature, TK, signals the onset of local singlet formation, while Fermi liquid coherence sets in only below a lower scale, T ⋆ . At low conduction electron density nc ("exhaustion" limit) , the ratio T ⋆ /TK is much smaller than unity, and is shown to depend only on nc and not on the Kondo coupling. The physical meaning of these two scales is demonstrated by computing several quantities as a function of nc and temperature.

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The conductance through a molecular device including electron-electron and electron-phonon interactions is calculated using the numerical renormalization group method. At low temperatures and weak electron-phonon coupling the properties of the conductance can be explained in terms of the standard Kondo model with renormalized parameters. At large electron-phonon coupling a charge analog of the Kondo effect takes place that can be mapped into an anisotropic Kondo model. In this regime the molecule is strongly polarized by a gate voltage which leads to rectification in the current-voltage characteristics of the molecular junction.

The effect of a magnetic field on the equilibrium spectral and transport properties of a singlemolecule junction is studied using the numerical renormalization group method. The molecule is described by the Anderson-Holstein model in which a single vibrational mode is coupled to the electron density. The effect of an applied magnetic field on the conductance in the Kondo regime is qualitatively different in the weak and strong electron-phonon coupling regimes. In the former case, the Kondo resonance is split and the conductance is strongly suppressed by a magnetic field gµBB kBTK, with TK the Kondo temperature. In the strong electron-phonon coupling regime a charge analog of the Kondo effect develops. In this case the Kondo resonance is not split by the field and the conductance in the Kondo regime is enhanced in a broad range of values of B.

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We study the competition between the Kondo effect and frustrating exchange interactions in a Kondo-lattice model within a large-N dynamical mean-field theory. We find a T = 0 phase transition between a heavy Fermi-liquid and a spin-liquid for a critical value of the exchange Jc = T 0 K , the single-impurity Kondo temperature. Close to the critical point, the Fermi liquid coherence scale T ⋆ is strongly reduced and the effective mass strongly enhanced. The regime T > T ⋆ is characterized by spin-liquid magnetic correlations and non-Fermi-liquid properties. It is suggested that magnetic frustration is a general mechanism which is essential to explain the large effective mass of some metallic compounds such as LiV2O4.

The linear transport properties of a model molecular transistor with electron-electron and electron-phonon interactions were investigated analytically and numerically. The model takes into account phonon modulation of the electronic energy levels and of the tunnelling barrier between the molecule and the electrodes. When both effects are present they lead to asymmetries in the dependence of the conductance on gate voltage. The Kondo effect is observed in the presence of electron-phonon interactions. There are important qualitative differences between the cases of weak and strong coupling. In the first case the standard Kondo effect driven by spin fluctuations occurs. In the second case, it is driven by charge fluctuations. The Fermi-liquid relation between the spectral density of the molecule and its charge is altered by electron-phonon interactions. Remarkably, the relation between the zero-temperature conductance and the charge remains unchanged. Therefore, there is perfect transmission in all regimes whenever the average number of electrons in the molecule is an odd integer.Comment: 9 pages, 6 figure