A. Martin-Rodero

The signature of chemical valence in the electrical conduction through a single-atom contact

Fabrication of structures at the atomic scale is now possible using state-of-the-art techniques for manipulating individual atoms, and it may become possible to design electrical circuits atom by atom. A prerequisite for successful design is a knowledge of the relationship between the macroscopic electrical characteristics of such circuits and the quantum properties of the individual atoms used as building blocks. As a first step, we show here that the chemical valence determines the conduction properties of the simplest imaginable circuit—a one-atom contact between two metallic banks. The extended quantum states that carry the current from one bank to the other necessarily proceed through the valence orbitals of the constriction atom. It thus seems reasonable to conjecture that the number of current-carrying modes (or ‘channels’) of a one-atom contact is determined by the number of available valence orbitals, and so should strongly differ for metallic elements in different series of the periodic table. We have tested this conjecture using scanning tunnelling microscopy and mechanically controllable break-junction techniques, to obtain atomic-size constrictions for four different metallic elements (Pb, Al, Nb and Au), covering a broad range of valences and orbital structures. Our results demonstrate unambiguously a direct link between valence orbitals and the number of conduction channels in one-atom contacts.

HAMILTONIAN APPROACH TO THE TRANSPORT PROPERTIES OF SUPERCONDUCTING QUANTUM POINT CONTACTS

A microscopic theory of the transport properties of quantum point contacts giving a unified description of the normal conductor-superconductor (N-S) and superconductor-superconductor (S-S) cases is presented. It is based on a model Hamiltonian describing charge transfer processes in the contact region and makes use of nonequilibrium Green function techniques for the calculation of the relevant quantities. It is explicitly shown that when calculations are performed up to infinite order in the coupling between the electrodes, the theory contains all known results predicted by the more usual scattering approach for N-S and S-S contacts. For the latter we introduce a specific formulation for dealing with the nonstationary transport properties. An efficient algorithm is developed for obtaining the dc and ac current components, which allows a detailed analysis of the different current-voltage characteristics for all range of parameters. We finally address the less understood small bias limit, for which some analytical results can be obtained within the present formalism. It is shown that four different physical regimes can be reached in this limit depending on the values of the inelastic scattering rate and the contact transmission. The behavior of the system in these regimes is discussed together with the conditions for their experimental observability. @S0163-1829~96!02034-6#

Microscopic Origin of Conducting Channels in Metallic Atomic-Size Contacts

We present a theoretical approach which allows to determine the number and orbital character of the conducting channels in metallic atomic contacts. We show how the conducting channels arise from the atomic orbitals having a significant contribution to the bands around the Fermi level. Our theory predicts that the number of conducting channels with non negligible transmission is 3 for Al and 5 for Nb one-atom contacts, in agreement with recent experiments. These results are shown to be robust with respect to disorder. The experimental values of the channels transmissions lie within the calculated distributions.

Electron correlation resonances in the transport through a single quantum level.

Correlation effects in the transport properties of a single quantum level coupled to electron reservoirs are discussed theoretically using a nonequilibrium Green function approach. Our method is based on the introduction of a second-order self-energy associated with the Coulomb interaction that consistently eliminates the pathologies of previous perturbative calculations. We present results for the current-voltage characteristic illustrating the different correlation effects that may be found in this system, including the Kondo anomaly and Coulomb blockade. We discuss the experimental conditions for the simultaneous observation of these effects in an ultrasmall quantum dot

Josephson and Andreev transport through quantum dots

In this article, we review the state of the art on the transport properties of quantum dot systems connected to superconducting and normal electrodes. The review is mainly focused on the theoretical achievements, although a summary of the most relevant experimental results is also given. A large part of the discussion is devoted to the single-level Anderson-type models generalized to include superconductivity in the leads, which already contains most of the interesting physical phenomena. Particular attention is paid to the competition between pairing and Kondo correlations, the emergence of π-junction behavior, the interplay of Andreev and resonant tunneling, and the important role of Andreev bound states that characterized the spectral properties of most of these systems. We give technical details on the several different analytical and numerical methods which have been developed for describing these properties. We further discuss the recent theoretical efforts devoted to extend this analysis to more complex situations like multidot, multilevel or multiterminal configurations in which novel phenomena is expected to emerge. These include control of the localized spin states by a Josephson current and also the possibility of creating entangled electron pairs by means of non-local Andreev processes.

Josephson current through a correlated quantum level: Andreev states and π junction behavior

The Josephson transport and the electronic properties of a quantum dot characterized by a single level coupled to superconducting leads is analyzed. Different approximations are used and compared: the mean-field approximation, the second-order perturbation theory in the Coulomb interaction, and the exact diagonalization in the zero bandwidth limit. The system exhibits a rich behavior as a function of the relevant parameters. We discuss in detail the conditions for the observation of π junction behavior and the effect of Coulomb interactions on the Andreev states.

Kondo effect in Normal-Superconductor Quantum Dots

We study the transport properties of a quantum dot coupled to a normal and a superconducting lead. The dot is represented by a generalized Anderson model. Correlation effects are taken into account by an appropriate selfenergy which interpolates between the limits of weak and strong coupling to the leads. The transport properties of the system are controlled by the interplay between the Kondo effect and Andreev reflection processes. We show that, depending on the parameters range the conductance can either be enhanced or suppressed as compared to the normal case. In particular, by adequately tunning the coupling to the leads one can reach the maximum value 4e 2 /h for the conductance.

Conductance quantization and electron resonances in sharp tips and atomic-size contacts

The electronic and transport properties of atomic-size contacts are analyzed theoretically using a self-consistent tight-binding model. Our results show that, for

Entangled Andreev pairs and collective excitations in nanoscale superconductors

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Universal features of electron-phonon interactions in atomic wires

-like metals, a sufficiently narrow contact exhibits well defined resonant states at the Fermi energy, spatially localized in the neck region. These states are robust with respect to disorder and provide a simple explanation for the observed tendency to conductance quantization. It is also shown that these properties disappear for a sufficiently large contact area. The possible relevance of the resonant states in scanning tunneling spectroscopy using sharp tips is briefly discussed.