Universal distribution of Kondo temperatures in dirty metals.

Kondo screening of diluted magnetic impurities in a disordered host is studied analytically and numerically in one, two, and three dimensions. It is shown that in the T(K) --> 0 limit the distribution of Kondo temperatures has a universal form P(T(K)) approximately T(K) (-a) that holds in the insulating phase and persists in the metallic phase close to the metal-insulator transition. Moreover, the exponent depends only on the dimensionality. The most important consequence of this result is that the T dependence of thermodynamic properties is smooth across the metal-insulator transition in three dimensional systems.

Magnetic quantum phase transitions in Kondo lattices.

The identification of magnetic quantum critical points in heavy fermion metals has provided an ideal setting for experimentally studying quantum criticality. Motivated by these experiments, considerable theoretical efforts have recently been devoted to re-examining the interplay between Kondo screening and magnetic interactions in Kondo lattice systems. A local quantum critical picture has emerged, in which magnetic interactions suppress Kondo screening precisely at the magnetic quantum critical point (QCP). The Fermi surface undergoes a large reconstruction across the QCP and the coherence scale of the Kondo lattice vanishes at the QCP. The dynamical spin susceptibility exhibits ω/T scaling and non-trivial exponents describe the temperature and frequency dependences of various physical quantities. These properties are to be contrasted with the conventional spin density wave picture, in which the Kondo screening is not suppressed at the QCP and the Fermi surface evolves smoothly across the phase transition. In this article we discuss recent microscopic studies of Kondo lattices within an extended dynamical mean field theory (EDMFT). We summarize the earlier work based on an analytical ϵ-expansion renormalization group method, and expand on the more recent numerical results. We also discuss the issues that have been raised concerning the magnetic phase diagram. We show that the zero-temperature magnetic transition is second order when double counting of the Ruderman-Kittel-Kasuya-Yosida interactions is avoided in EDMFT.

Many-body effects on the transport properties of single-molecule devices.

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.

Continuous quantum phase transition in a Kndo lattice model.

We study the magnetic quantum phase transition in an anisotropic Kondo lattice model. The dynamical competition between the RKKY and Kondo interactions is treated using an extended dynamic mean field theory appropriate for both the antiferromagnetic and paramagnetic phases. A quantum Monte Carlo approach is used, which is able to reach very low temperatures, of the order of 1% of the bare Kondo scale. We find that the finite-temperature magnetic transition, which occurs for sufficiently large RKKY interactions, is first order. The extrapolated zero-temperature magnetic transition, on the other hand, is continuous and locally critical.

Locally critical point in an anisotropic Kondo lattice.

We report the first numerical identification of a locally quantum critical point at which the criticality of the local Kondo physics is embedded in that associated with a magnetic ordering. We are able to numerically access the quantum critical behavior by focusing on a Kondo-lattice model with Ising anisotropy. We also establish that the critical exponent for the q-dependent dynamical spin susceptibility is fractional and compares well with the experimental value for heavy fermions.

Non-fermi-liquid scaling in Ce(Ru0.5Rh)2Si2.

We study the temperature and field dependence of the magnetic and transport properties of the non-Fermi-liquid (NFL) compound Ce(Ru0.5Rh0.5)2Si2. For fields H less, similar0.1 T the results suggest that the observed NFL behavior is disorder driven. For higher fields, however, magnetic and transport properties are dominated by the coupling of the conduction electrons to critical spin fluctuations. The temperature dependence of the susceptibility as well as the scaling properties of the magnetoresistance are in very good agreement with the predictions of recent dynamical mean-field theories of Kondo alloys close to a spin-glass quantum critical point.