Shot noise in tunneling transport through molecules and quantum dots

We consider electrical transport through single molecules coupled to metal electrodes via tunneling barriers. Approximating the molecule by the Anderson impurity model as the simplest model which includes Coulomb charging effects, we extend the ``orthodox'' theory to expand current and shot noise systematically order by order in the tunnel couplings. In particular, we show that a combined measurement of current and shot noise reveals detailed information of the system even in the weak-coupling limit, such as the ratio of the tunnel-coupling strengths of the molecule to the left and right electrode, and the presence of the Coulomb charging energy. Our analysis holds for single-level quantum dots as well.Comment: 8 page

A note on cluster methods for strongly correlated electron systems

We develop, clarify and test various aspects of cluster methods dynamical mean field methods using a soluble toy model as a benchmark. We find that the Cellular Dynamical Mean Field Theory (C-DMFT) converges very rapidly and compare its convergence properties with those of the Dynamical Cluster Approximation (DCA). We propose and test improved estimators for the lattice self energy within C-DMFT.Comment: 5 pages, 3 figures; major change

A novel FLEX supplemented QMC approach to the Hubbard model

This paper introduces a novel ansatz-based technique for solution of the Hubbard model over two length scales. Short range correlations are treated exactly using a dynamical cluster approximation QMC simulation, while longer-length-scale physics requiring larger cluster sizes is incorporated through the introduction of the fluctuation exchange (FLEX) approximation. The properties of the resulting hybrid scheme are examined, and the description of local moment formation is compared to exact results in 1D. The effects of electron-electron coupling and electron doping on the shape of the Fermi-surface are demonstrated in 2D. Causality is examined in both 1D and 2D. We find that the scheme is successful if QMC clusters of $N_C\ge 4$ are used (with sufficiently high temperatures in 1D), however very small QMC clusters of $N_C=1$ lead to acausal results

Towards analytical approaches to the dynamical-cluster approximation

I introduce several simplified schemes for the approximation of the self-consistency condition of the dynamical cluster approximation. The applicability of the schemes is tested numerically using the fluctuation-exchange approximation as a cluster solver for the Hubbard model. Thermodynamic properties are found to be practically indistinguishable from those computed using the full self-consistent scheme in all cases where the non-interacting partial density of states is replaced by simplified analytic forms with matching 1st and 2nd moments. Green functions are also compared and found to be in close agreement, and the density of states computed using Pad\'{e} approximant analytic continuation shows that dynamical properties can also be approximated effectively. Extensions to two-particle properties and multiple bands are discussed. Simplified approaches to the dynamical cluster approximation should lead to new analytic solutions of the Hubbard and other models

ARPES Spectra of the Hubbard model

We discuss spectra calculated for the 2D Hubbard model in the intermediate coupling regime with the dynamical cluster approximation, which is a non-perturbative approach. We find a crossover from a normal Fermi liquid with a Fermi surface closed around the Brillouin zone center at large doping to a non-Fermi liquid for small doping. The crossover is signalled by a splitting of the Fermi surface around the $X$ point of the 2D Brillouin zone, which eventually leads to a hole-like Fermi surface closed around the point M. The topology of the Fermi surface at low doping indicates a violation of Luttinger's theorem. We discuss different ways of presenting the spectral data to extract information about the Fermi surface. A comparison to recent experiments will be presented.Comment: 8 pages, 7 color figures, uses RevTeX

Fictive Impurity Models: an Alternative Formulation of the Cluster Dynamical Mean Field Method

"Cluster" extensions of the dynamical mean field method to include longer range correlations are discussed. It is argued that the clusters arising in these methods are naturally interpreted not as actual subunits of a physical lattice but as algorithms for computing coefficients in an orthogonal function expansion of the momentum dependence of the electronic self-energy. The difficulties with causality which have been found to plague cluster dynamical mean field methods are shown to be related to the "ringing" phenomenon familiar from Fourier analysis. The analogy is used to motivate proposals for simple filtering methods to circumvent them. The formalism is tested by comparison to low order perturbative calculations and self consistent solutions

Dynamical 1/N approach to time-dependent currents through quantum dots

A systematic truncation of the many-body Hilbert space is implemented to study how electrons in a quantum dot attached to conducting leads respond to time-dependent biases. The method, which we call the dynamical 1/N approach, is first tested in the most unfavorable case, the case of spinless fermions (N=1). We recover the expected behavior, including transient ringing of the current in response to an abrupt change of bias. We then apply the approach to the physical case of spinning electrons, N=2, in the Kondo regime for the case of infinite intradot Coulomb repulsion. In agreement with previous calculations based on the non-crossing approximation (NCA), we find current oscillations associated with transitions between Kondo resonances situated at the Fermi levels of each lead. We show that this behavior persists for a more realistic model of semiconducting quantum dots in which the Coulomb repulsion is finite.Comment: 18 pages, 7 eps figures, discussion extended for spinless electrons and typo

The Korringa-Kohn-Rostoker Non-Local Coherent Potential Approximation (KKR-NLCPA)

We introduce the Korringa-Kohn-Rostocker non-local coherent potential approximation (KKR-NLCPA) for describing the electronic structure of disordered systems. The KKR-NLCPA systematically provides a hierarchy of improvements upon the widely used KKR-CPA approach and includes non-local correlations in the disorder configurations by means of a self-consistently embedded cluster. The KKR-NLCPA method satisfies all of the requirements for a successful cluster generalization of the KKR-CPA; it remains fully causal, becomes exact in the limit of large cluster sizes, reduces to the KKR-CPA for a single-site cluster, is straightforward to implement numerically, and enables the effects of short-range order upon the electronic structure to be investigated. In particular, it is suitable for combination with electronic density functional theory to give an ab-initio description of disordered systems. Future applications to charge correlation and lattice displacement effects in alloys and spin fluctuations in magnets amongst others are very promising. We illustrate the method by application to a simple one-dimensional model.Comment: Revised versio