Alfredo Levy Yeyati

Quantum properties of atomic-sized conductors

Abstract Using remarkably simple experimental techniques it is possible to gently break a metallic contact and thus form conducting nanowires. During the last stages of the pulling a neck-shaped wire connects the two electrodes, the diameter of which is reduced to single atom upon further stretching. For some metals it is even possible to form a chain of individual atoms in this fashion. Although the atomic structure of contacts can be quite complicated, as soon as the weakest point is reduced to just a single atom the complexity is removed. The properties of the contact are then dominantly determined by the nature of this atom. This has allowed for quantitative comparison of theory and experiment for many properties, and atomic contacts have proven to form a rich test-bed for concepts from mesoscopic physics. Properties investigated include multiple Andreev reflection, shot noise, conductance quantization, conductance fluctuations, and dynamical Coulomb blockade. In addition, pronounced quantum effects show up in the mechanical properties of the contacts, as seen in the force and cohesion energy of the nanowires. We review this research, which has been performed mainly during the past decade, and we discuss the results in the context of related developments.

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

Scattering phases in quantum dots : an analysis based on lattice models

The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum rule and discuss the deviation of the phase of the transmission amplitude from the Friedel phase at the zeroes of the transmission. The occurrence of such zeroes is related to the parity of the isolated dot levels. A statistical analysis of the isolated dot wave-functions reveals the absence of significant correlations in the parity for large disorder and the appearance, for weak disorder, of certain dot states which are strongly coupled to the leads. It is shown that large differences in the coupling to the leads give rise to an anomalous charging of the dot levels. A mechanism for the phase lapse observed experimentally based on this property is discussed and illustrated with model calculations.

TRANSPORT IN MULTILEVEL QUANTUM DOTS : FROM THE KONDO EFFECT TO THE COULOMB BLOCKADE REGIME

A new theoretical method is introduced to study coherent electron transport in an interacting multilevel quantum dot. The method yields the correct behavior both in the limit of weak and strong coupling to the leads, giving a unified description of Coulomb blockade and the Kondo effect. Results for the density of states and the temperature dependent conductance for a two- level dot are presented. The relevance of these results in connection to recent experiments on the Kondo effect in semiconducting quantum dots is discussed.

Entanglement Detection from Conductance Measurements in Carbon Nanotube Cooper Pair Splitters

Spin-orbit interaction provides a spin filtering effect in carbon nanotube based Cooper pair splitters that allows us to determine spin correlators directly from current measurements. The spin filtering axes are tunable by a global external magnetic field. By a bending of the nanotube, the filtering axes on both sides of the Cooper pair splitter become sufficiently different that a test of entanglement of the injected Cooper pairs through a Bell-like inequality can be implemented. This implementation does not require noise measurements, supports imperfect splitting efficiency and disorder, and does not demand a full knowledge of the spin-orbit strength. Using a microscopic calculation we demonstrate that entanglement detection by violation of the Bell-like inequality is within the reach of current experimental setups.

Subradiant split Cooper pairs.

We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of cavity quantum electrodynamics could be generalized to many other nanoscale circuits.

Shot Noise and Coherent Multiple Charge Transfer in Superconducting Quantum Point-Contacts

We analyze the shot noise in a voltage biased superconducting quantum point-contact. Results are presented for the single channel case with arbitrary transmission. In the limit of very low transmission it is found that the effective charge, defined from the noise-current ratio, exhibits a step-like behavior as a function of voltage with well defined plateaus at integer values of the electronic charge. This multiple charge corresponds to the transmitted charge in a Multiple Andreev Reflection (MAR) process. This effect gradually disappears for increasing transmission due to interference between different MAR processes.

Nonadiabatic features of electron pumping through a quantum dot in the Kondo regime

We investigate the behavior of the dc electronic current, Jdc, in an interacting quantum dot driven by two ac local potentials oscillating with a frequency, Omega0, and a phase-lag, phi. We provide analytical functions to describe the fingerprints of the Coulomb interaction in an experimental Jdc vs phi characteristic curve. We show that the Kondo resonance reduces at low temperatures the frequency range for the linear behavior of Jdc in Omega0 to take place and determines the evolution of the dc-current as the temperature increases.