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The concept of a Thouless energy, introduced originally in the context of Anderson localization (as the inverse diffusion time through a finite-size disordered conductor), has turned out to be an essential energy scale for understanding proximity-induced superconductivity in a normal metal connected to a superconductor; in particular, it has had significant success in the quasiclassical description of phenomena in superconductor-normal-metal-superconductor Josephson junctions. We generalize the concept of a Thouless energy to include transport through strongly correlated insulators, and show how it provides a unified description of transport and indicates how the quasiclassical picture breaks down as we turn on electron-electron correlations in the normal metal layer of a Josephson junction to tune it through the Mott metal-insulator transition.

Monte Carlo-maximum entropy calculations of the conductivity of the infinite-dimensional periodic Anderson model are presented. We show that the optical conductivity displays anomalies associated with the exhaustion of conduction-band states near the Fermi energy including a Drude weight which rises with temperature, with weight transferred from a temperature and doping-dependent mid-IR peak and a low-frequency incoherent contribution. Both the Drude and mid-IR peaks persist up to very high temperatures. The resistivity displays a non-universal peak and two other regions associated with impurity-like physics at high temperatures and Fermi Liquid formation at low T., 6 pages, 4 figures, To appear in Phys. Rev. B

Employing a quantum Monte Carlo simulation we find a pairing instability in the normal state of the infinite dimensional periodic Anderson model. Superconductivity arises from a normal state in which the screening is protracted and which is clearly not a Fermi liquid. The phase diagram is reentrant reflecting competition between superconductivity and Fermi liquid formation. The estimated superconducting order parameter is even, but has nodes as a function of frequency. This opens the possibility of a temporal node and an effective order parameter composed of charge pairs and spin excitations., one postscript file, 6 pages including 6 figures. To appear in Phil. Mag. B

The Thouless energy was introduced in the 1970s as a semiclassical energy for electrons diffusing through a finite-sized conductor. It turns out to be an important quantum-mechanical energy scale for many systems ranging from disordered metals to quantum chaos to quantum chromodynamics. In particular, it has been quite successful in describing the properties of Josephson junctions when the barrier is a diffusive normal-state metal. The Thouless energy concept can be generalized to insulating barriers by extracting an energy scale from the two-probe Kubo conductance of a strongly correlated electron system metallic or insulating via a generalized definition of the quantum-mechanical level spacing to many-body systems. This energy scale is known to determine the crossover from tunneling to Ohmic thermally activated transport in normal tunnel junctions. Here we use it to illustrate how the quasiclassical picture of transport in Josephson junctions is modified as the strongly correlated barrier passes through the Mott transition. Surprisingly, we find the quasiclassical form holds well beyond its putative realm of validity.

We study the pseudogaps in the spectra of the 2D Hubbard model using both finite-size and dynamical cluster approximation (DCA) quantum Monte Carlo calculations. At half-filling, a charge pseudogap, accompanied by non-Fermi-liquid behavior in the self-energy, is shown to persist in the thermodynamic limit. The DCA (finite-size) method systematically underestimates (overestimates) the width of the pseudogap. A spin pseudogap is not seen at half-filling. At finite doping, a divergent d-wave pair susceptibility is observed.

The Dynamical Cluster Approximation (DCA) is used to study non-local corrections to the dynamical mean field phase diagram of the two-dimensional Hubbard model. Regions of antiferromagnetic, d-wave superconducting, pseudo-gapped non-Fermi liquid, and Fermi liquid behaviors are found, in rough agreement with the generic phase diagram of the cuprates. The non-local fluctuations beyond the mean field both suppress the antiferromagnetism and mediate the superconductivity., 4 pages, 5 eps figures, submitted to PRL

We discuss the "exhaustion" problem in the context of the Periodic Anderson Model using Iterated Perturbation Theory(IPT) within the Dynamical Mean Field Theory. We find that, despite its limitations, IPT captures the exhaustion physics, which manifests itself as a dramatic, strongly energy dependent suppression of the effective Anderson impurity problem. As a consequence, low energy scales in the lattice case are strongly suppressed compared to the "Kondo scale" in the single-impurity picture. The IPT results are in qualitative agreement with recent Quantum Monte Carlo results for the same problem., Comment: 13 preprint pages including 1 table and 4 eps figures, replaced by revised version, accepted for publication in Europhysics Letters, added references and content

Publisher Summary This chapter discusses photoelectron spectroscopy (PES) in heavy fermion systems. The theoretical aspects of single-impurity model (SIM) and its calculational approximations Guunarsson-Schonhammer (GS), non-crossing approximation (NCA), as well as various screening models and new pairing approaches are discussed. This is followed by a summary of NCA predictions for PES. The recent calculations of the periodic Anderson model and its application to photoemission are discussed. The chapter reviews the single-crystal data, both on Ce and Yb compounds, and test for the applicability of SIM in periodic systems. This is followed by a discussion of data that suggests that at least in Ce compounds the 4f states form very narrow, weakly temperature dependent bands, not inconsistent with the periodic Anderson model (PAM). The chapter considers heavy fermions within the 5f series of elements (primarily U) and emphasizes the similarities with and differences from the 4f series.

The unusual properties of heavy fermion (or heavy electron) materials have sparked an avalanche of research over the last two decades in order to understand the basic phenomena responsible for these properties. The reader is referred to numerous review articles, such as Fisk et al., (1995), Grewe and Steglich (1991), Hess et al., (1993), Lawrence and Mills (1991), Ott and Fisk (1987), Stewart (1984), Thompson and Lawrence (1994). The term heavy fermion refers to materials (thus far only compounds with elements having an unfilled 4f or 5f shells) whose electronic properties suggest that the conduction electrons have a very heavy effective mass. This is inferred from the linear term in the low specific heat (Cp = γT+ OT2) which usually has an upturn at low temperatures and suggests [some of the first discoveries were by Andres et al. (1975), followed by Steglich (1979), Stewart et al (1984), Ott et al. (1983)1 y-values as large as 1500 mJ/mole-K2. deHaas-van Alphen measurements have confirmed the existence of heavy masses [Springford and Reinders (1988), Lonzarich (1988), Onuki (1993)1. The quadratic term in the resistivity and the Pauli susceptibility also indicate the existence of a mass enhancement. It is well established that indeed it is the f-electrons that are responsible for the unusual properties [Grewe and Steglich (1991)].

The electronic structure of both Ce and U heavy fermions appears to consist of extremely narrow, nearly temperature independent bands (i.e., no spectral weight loss or transfer with temperature). A small dispersion of the f-bands above the Kondo temperature is easily measurable so that a Kondo resonance, as defined by NCA, is not evident. Preliminary results, however, indicate that the Periodic Anderson Model captures some of the essential physics. Angle-integrated resonant photoemission results on {delta}-Pu indicate a narrow 5f feature at E{sub F}, similar in width to f-states in Ce and U compounds, but differing in that cross-section behavior of the near-E{sub F} feature suggests substantial 6D admixture.

We introduce an extension of the dynamical mean field approximation (DMFA) which retains the causal properties and generality of the DMFA, but allows for systematic inclusion of non-local corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA (exact result) is recovered as the cluster size goes to one (infinity). As a demonstration, we study the Falicov-Kimball model using a variety of cluster sizes. We show that the sum rules are preserved, the spectra are positive definite, and the non-local correlations suppress the CDW transition temperature. \, 4 pages, including 4 figures The problems with convergence and causality have been positively resolved. Two figures have been changed

We present numerically exact predictions of the periodic and single-impurity Anderson models to address photoemission experiments on heavy Fermion systems. Unlike the single impurity model the lattice model is able to account for the enhanced intensity, dispersion, and apparent weak temperature dependence of the Kondo resonant peak seen in recent controversial photoemission experiments. We present a consistent interpretation of these results as a crossover from the impurity regime to an effective Hubbard model regime described by Nozieres., 4 pages, 3 figures

A local, second-order (truncated) approximation is applied to the Hubbard model in three dimensions. Lowering the temperature, at half-filling, the paramagnetic ground state becomes unstable towards the formation of a commensurate spin-density-wave (SDW) state (antiferromagnetism) and sufficiently far away from half-filling towards the formation of incommensurate SDW states. The incommensurate-ordering wavevector does not deviate much from the commensurate one, which is in accord with the experimental data for the SDW in chromium alloys., plain tex, 16 pages, 5 Postscript figures

The asymmetric infinite-dimensional periodic Anderson model is examined with a quantum Monte Carlo simulation. For small conduction band filling, we find a severe reduction in the Kondo scale, compared to the impurity value, as well as protracted spin screening consistent with some recent controversial photoemission experiments. The Kondo screening drives a ferromagnetic transition when the conduction band is quarter-filled and both the RKKY and superexchange favor antiferromagnetism. We also find RKKY-driven ferromagnetic and antiferromagnetic transitions., Comment: 5 pages, LaTeX and 4 PS figures