Electronic transport properties of single-molecule junctions have been widely measured by several techniques, including mechanically controllable break junctions, electromigration break junctions, and by means of scanning tunneling microscopes. In parallel, many theoretical tools have been developed and refined for describing such transport properties and for obtaining numerical predictions. Most prominent among these theoretical tools are those based upon density functional theory. In this review, theory and experiment are critically compared, and this confrontation leads to several important conclusions. The theoretically predicted trends nowadays reproduce the experimental findings well for series of molecules with a single well-defined control parameter, such as the length of the molecules. The quantitative agreement between theory and experiment usually is less convincing, however. Two main sources for the quantitative discrepancies can be identified. Experimentally, the atomic structure of the junction typically realized in the measurement is not well known, so simulations rely on plausible scenarios. In theory, correlation effects can be included only in approximations that are difficult to control for experimentally relevant situations. Therefore, one typically expects qualitative agreement with present modeling tools; in exceptional cases a quantitative agreement has already been achieved. For further progress, benchmark systems are required that are sufficiently well defined by experiment to allow quantitative testing of the approximation schemes underlying the theoretical modeling. Several key experiments can be identified suggesting that the present description may even be qualitatively incomplete in some cases. Such key experimental observations and their current models are also discussed here, leading to several suggestions for extensions of the models toward including dynamic image charges, electron correlations, and polaron formation.

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Advances and challenges in single-molecule electron transport

Magnetic ordering in TbRh2Si2 and CeRh2Si2

If the d–f exchange interaction is taken as the driving attractive interaction for a non-phonon hybrid pairing mechanism one gets results of surprising significance for heavy Fermion superconductors: a transition temperature one order of magnitude smaller than the single ion Kondo temperature, a large critical field initial slope, and a huge specific heat jump, whereas the ratio of the gap at zero temperature to kTc has the BCS value 3.53. Except for the relation between Tc and the Kondo temperature these statements remain to be true for any other hybrid pairing interaction of the same form.



Wenn die d–f-Austauschwechselwirkung als die wirkende anziehende Wechselwirkung fur einen Nicht-Phonon-Hybridpaarungsmechanismus angeschen wird, erhalt man Ergebnisse von uberraschender Bedeutung fur schwere Fermionen-Supraleiter: eine Ubergangstemperatur, die eine Grosenordnung geringer als die Einionen-Kondo-Temperatur ist, einen grosen Anfangsanstieg des kritischen Feldes und einen grosen Sprung der spezifischen Warme, wahrend das Verhaltnis der Energielucke bei der Temperatur null zu kTc den BCS-Wert 3,53 hat. Auser fur die Beziehung zwischen Tc und der Kondotemperatur bleiben diese Feststellungen gultig fur jede andere Paarungswechselwirkung derselben Form.

Hybrid Pairing and Heavy Fermions

For the periodic Anderson model in the strong correlation regime, we construct the effective Hamiltonian Heff up to terms of the fourth order in the parameter V/U, where V is the hybridization interaction intensity and U is the intra-atom Coulomb repulsion strength. This Hamiltonian contains interactions inducing both magnetic ordering and Cooper instability under conditions of a mixed valency of rare-earth ions. Based on numerical calculations, we obtain information about the dependences of the effective interaction parameters on the distance between crystal lattice sites. We demonstrate that realizing exchange interactions corresponds to a strongly frustrated system of localized spin moments and facilitates the suppression of the antiferromagnetic order parameter with a possible transition to the state of a quantum spin liquid. It is essential that among the terms in Heff inducing the transition to the superconductivity phase, there are terms resulting in the d-type symmetry of the superconductivity order parameter; such a symmetry is realized in many heavy-fermion compounds.

Effective interactions in the periodic Anderson model in the regime of mixed valency with strong correlations

Starting from tight binding Hamiltonians with strong short range Coulomb interactions we show how to derive a description where the fermions with short range Coulomb repulsion are replaced by pure localised spins and the remaining fermionic degrees of freedom are modified to take into account the charge degrees of freedom that the spin operators treated as fermions initially possessed. To leading order we find the Kondo Lattice, a single particle fermion Hamiltonian together with an exchange term between the localised spin and the fermion spin operator. At the next order, if we assume that the localised spins are random, we find a many body attraction between singlet pairs of fermions and non-linear-hopping terms. We analyse the spin half Anderson Lattice and find an attraction for pairs of electrons which sit on the same site but competing with this is a loss in mobility due to the non-linear-hopping if the electrons do pair. We also analyse a ‘HighT

 c
 ’ model where we find attraction between pairs of Oxygenp-electrons both on the same site and on neighbouring Oxygen sites due to enhanced hopping between these sites.

Near the Kondo limit of the Anderson lattice: spins, fermions and high ‘ T c ’

A canonical transformation of the Schrieffer-Wolff type is applied to the periodic Anderson model. The case of infinitely correlated $f$-like orbitals is dealt with, and these are described through standard basis operators, including spin degeneracy only. First- and third-order terms in the mixing parameter are eliminated. The resulting Hamiltonian contains terms up to fourth order. These describe several interaction processes including intersite spin and charge correlations, conduction-electron scattering, and excitonic interactions. A detailed analysis of the modified Ruderman-Kittel-Kasuya-Yosida interaction obtained is given. Possible extensions of some of the results to higher orders are discussed. The method provides a way to evaluate the spin and charge susceptibilities of the conduction-electron gas in this model. The possible relevance of these functions to a theory of the phonon spectrum and of magnetic ordering of intermediate-valence systems is mentioned.

César Proetto

Papers

Fourth-order effective Hamiltonian for the Anderson lattice

Narrow band limit of the equivalence between Anderson and Kondo Hamiltonians