arXiv subjects

M. H. Hettler

Publications and source records attributed to M. H. Hettler.

15 recordsLinked to original sources

arXiv2009

Pair-tunneling resonance in the single-electron transport regime

We predict a new electron pair-tunneling (PT) resonance in non-linear transport through quantum dots with positive charging energies exceeding the broadening due to thermal and quantum fluctuations. The PT resonance shows up in the single-electron transport (SET) regime as a peak in the derivative of the non-linear conductance when the electrochemical potential of one electrode matches the average of two subsequent charge addition energies. For a single level quantum dot (Anderson model) we find the analytic peak shape and the dependence on temperature, magnetic field and junction asymmetry and compare with the inelastic cotunneling peak which is of the same order of magnitude. In experimental transport data the PT resonance may be mistaken for a weak SET resonance judging only by the voltage dependence of its position. Our results provide essential clues to avoid such erroneous interpretation of transport spectroscopy data.

cond-mat.mes-hall↗

arXiv2005

Strongly enhanced shot noise in chains of quantum dots

We study charge transport through a chain of quantum dots. The dots are fully coherent among each other and weakly coupled to metallic electrodes via the dots at the interface, thus modelling a molecular wire. If the non-local Coulomb interactions dominate over the inter-dot hopping we find strongly enhanced shot noise above the sequential tunneling threshold. The current is not enhanced in the region of enhanced noise, thus rendering the noise super-Poissonian. In contrast to earlier work this is achieved even in a fully symmetric system. The origin of this novel behavior lies in a competition of "slow" and "fast" transport channels that are formed due to the differing non-local wave functions and total spin of the states participating in transport. This strong enhancement may allow direct experimental detection of shot noise in a chain of lateral quantum dots.

cond-mat.mes-hall↗

arXiv2005

Co-tunneling current and shot noise in quantum dots

We derive general expressions for the current and shot noise, taking into account non-Markovian memory effects. In generalization of previous approaches our theory is valid for arbitrary Coulomb interaction and coupling strength and is applicable to quantum dots and more complex systems like molecules. A diagrammatic expansion up to second-order in the coupling strength, taking into account co-tunneling processes, allows for a study of transport in a regime relevant to many experiments. As an example, we consider a single-level quantum dot, focusing on the Coulomb-blockade regime. We find super-Poissonian shot noise due to spin-flip co-tunneling processes at an energy scale different from the one expected from first-order calculations, with a sensitive dependence on the coupling strength.

cond-mat.mes-hall↗

arXiv2004

Super-poissonian noise, negative differential conductance, and relaxation effects in transport through molecules, quantum dots and nanotubes

We consider charge transport through a nanoscopic object, e.g. single molecules, short nanotubes, or quantum dots, that is weakly coupled to metallic electrodes. We account for several levels of the molecule/quantum dot with level-dependent coupling strengths, and allow for relaxation of the excited states. The current-voltage characteristics as well as the current noise are calculated within first-order perturbation expansion in the coupling strengths. For the case of asymmetric coupling to the leads we predict negative-differential-conductance accompanied with super-poissonian noise. Both effects are destroyed by fast relaxation processes. The non-monotonic behavior of the shot noise as a function of bias and relaxation rate reflects the details of the electronic structure and level-dependent coupling strengths.

cond-mat.mes-hall↗

arXiv2004

Quantum Cluster Theories

Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative and are always in the thermodynamic limit. Their quality can be systematically improved, and they provide complementary information to finite size simulations. They have been studied intensively in recent years and are now well established. After a brief historical review, this article comparatively discusses the nature and advantages of these cluster techniques. Applications to common models of correlated electron systems are reviewed.

cond-mat.str-el↗

arXiv2002

Dynamical Cluster Approximation Employing FLEX as a Cluster Solver

We employ the Dynamical Cluster Approximation (DCA) in conjunction with the Fluctuation Exchange Approximation (FLEX) to study the Hubbard model. The DCA is a technique to systematically restore the momentum conservation at the internal vertices of Feynman diagrams relinquished in the Dynamical Mean Field Approximation (DMFA). FLEX is a perturbative diagrammatic approach in which classes of Feynman diagrams are summed over analytically using geometric series. The FLEX is used as a tool to investigate the complementarity of the DCA and the finite size lattice technique with periodic boundary conditions by comparing their results for the Hubbard model. We also study the microscopic theory underlying the DCA in terms of compact (skeletal) and non-compact diagrammatic contributions to the thermodynamic potential independent of a specific model. The significant advantages of the DCA implementation in momentum space suggests the development of the same formalism for the frequency space. However, we show that such a formalism for the Matsubara frequencies at finite temperatures leads to acausal results and is not viable. However, a real frequency approach is shown to be feasible.

cond-mat.str-el↗

arXiv2002

Current collapse in tunneling transport through benzene

We investigate the electrical transport through a system of benzene coupled to metal electrodes by electron tunneling. Using electronic structure calculations, a semi--quantitative model for the pi-electrons of the benzene is derived that includes general two-body interactions. After exact diagonalization of the benzene model the transport is computed using perturbation theory for weak electrode-benzene coupling (golden rule approximation). We include the effect of an applied electric field on the molecular states, as well as radiative relaxation. We predict a current collapse and strong negative differential conductance due to a ``blocking'' state when the electrode is coupled to the para-position of benzene. In contrast, for coupling to the meta-position, a series of steps in the I-V curve is found.

cond-mat.mes-hall↗

arXiv2002

Analysis of the dynamical cluster approximation for the Hubbard model

We examine a central approximation of the recently introduced Dynamical Cluster Approximation (DCA) by example of the Hubbard model. By both analytical and numerical means we study non-compact and compact contributions to the thermodynamic potential. We show that approximating non-compact diagrams by their cluster analogs results in a larger systematic error as compared to the compact diagrams. Consequently, only the compact contributions should be taken from the cluster, whereas non-compact graphs should be inferred from the appropriate Dyson equation. The distinction between non-compact and compact diagrams persists even in the limit of infinite dimensions. Non-local corrections beyond the DCA exist for the non-compact diagrams, whereas they vanish for compact diagrams.

cond-mat.str-el↗

arXiv2000

Phase Diagram of the Hubbard Model: Beyond the Dynamical Mean Field

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.

cond-mat.str-el↗

arXiv1999

The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems

We recently introduced the dynamical cluster approximation(DCA), a new technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite size periodic cluster. The dynamical mean field approximation (exact result) is obtained by taking the cluster to a single site (the thermodynamic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, $Φ$-derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a Quantum Monte Carlo and Exact Enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the CDW transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases.

cond-mat.str-el↗

arXiv1998

Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems

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. \

cond-mat.str-el↗

arXiv1998

Superconducting Instability in the Periodic Anderson Model

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.

cond-mat.str-el↗

arXiv1997

Non-equilibrium dynamics of the Anderson impurity model

The M-channel Anderson impurity model (M=1,2) is studied in the Kondo limit with a finite voltage bias applied to the conduction electron reservoirs. Using the Non-Crossing Approximation (NCA), we calculate the local spectral functions, the differential conductance, and susceptibility at non-zero bias for symmetric as well as asymmetric coupling of the impurity to the leads. We describe an effective procedure to solve the NCA integral equations which enables us to reach temperatures far below the Kondo scale. This allows us to study the scaling regime where the conductance depends on the bias only via a scaling function. Our results are applicable to both tunnel junctions and to point contacts. We present a general formula which allows one to go between the two cases of tunnel junctions and point contacts. Comparison is also made between the conformal field theory and the NCA conduction electron self-energies in the two channel case.

cond-mat.mes-hall↗

arXiv1997

Reply to the Comment by A.A. Nersesyan and A.M. Tsvelik on the "Non--Zero Fermi Level Density of States for a Disordered d-Wave Superconductor in Two Dimensions" (PRL 77, 3013 (1996)) by K. Ziegler, M.H. Hettler and P.J. Hirschfeld

In a recent Comment (cond-mat/9701197) on our Letter (PRL 77, 3013 (1996), cond-mat/9604176) Nersesyan and Tsvelik questioned the relevance of our exact calculation of the density of states (DOS) of a 2D d-wave superconductor using a Lorentzian disorder distribution, claiming ``that models with Lorentzian and Gaussian disorder belong to different universality classes'', on grounds of a comparison with a straightforward perturbation expansion in the disorder potential. We showed in a very recent paper (cond-mat/9703047) that a rigorous nonzero lower bound for DOS can be established without relying on the tails of the disorder distribution, i.e. both the Gaussian and Lorentzian distributions belong to a large class of distributions which give a nonzero lower bound for the DOS. This proves that the result of our Letter is generic.

cond-mat.supr-con↗

arXiv1997

Lower Bound for the Fermi Level Density of States of a Disordered D-Wave Superconductor in Two Dimensions

We consider a disordered d--wave superconductor in two dimensions. Recently, we have shown in an exact calculation that for a lattice model with a Lorentzian distributed random chemical potential the quasiparticle density of states at the Fermi level is nonzero. As the exact result holds only for the special choice of the Lorentzian, we employ different methods to show that for a large class of distributions, including the Gaussian distribution, one can establish a nonzero lower bound for the Fermi level density of states. The fact that the tails of the distributions are unimportant in deriving the lower bound shows that the exact result obtained before is generic.

cond-mat.supr-con↗