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Impurities coupled to superconductors offer a controlled platform to understand the interplay between superconductivity, many-body interactions, and non-equilibrium physics. In the equilibrium situation, local interactions at the impurity induce a transition between the spin-singlet to the spin-doublet ground state, resulting in a supercurrent sign reversal ($0-\pi$ transition). In this work, we apply the exact time-dependent density matrix renormalization group method to simulate the transient dynamics of such superconducting systems. We also use a perturbative approximation to analyze their properties at longer times. These two methods agree for a wide range of parameters. In a phase-biased situation, the system gets trapped in a metastable state characterized by a lower supercurrent compared to the equilibrium case. We show that local Coulomb interactions do not provide an effective relaxation mechanism for the initially trapped quasiparticles. In contrast, other relaxation mechanisms, such as coupling to a third normal lead, make the impurity spin relax for parameter values corresponding to the equilibrium $0$ phase. For parameters corresponding to the equilibrium $\pi$ phase the impurity converges to a spin-polarized stationary state. Similar qualitative behavior is found for a voltage-biased junction, which provides an effective relaxation mechanism for the trapped quasiparticles in the junction., Comment: 13 pages, 12 figures

We investigate on the same footing the time-dependent electronic transport properties and vibrational dynamics of a molecular junction. We show that fluctuations of both the molecular vibron displacement and the electronic current across the junction undergo damped oscillations towards the steady-state. We assign the former to the onset of electron tunneling events assisted by vibron-emission. The time-dependent build-up of electron-hole correlations is revealed as a departure of the charge-transfer statistics from the generalized-binomial one after a critical time tc. The phonon-back action on the tunneling electrons is shown to amplify and accelerate this build-up mechanism.

We present an analysis of the transient electronic and transport properties of a nanojunction in the presence of electron-electron and electron-phonon interactions. We introduce a novel numerical approach which allows for an efficient evaluation of the non-equilibrium Green functions in the time domain. Within this approach we implement different self-consistent diagrammatic approximations in order to analyze the system evolution after a sudden connection to the leads and its convergence to the steady state. These approximations are tested by comparison with available numerically exact results, showing good agreement even for the case of large interaction strength. In addition to its methodological advantages, this approach allows us to study several issues of broad current interest like the build up in time of Kondo correlations and the presence or absence of bistability associated with electron-phonon interactions. We find that, in general, correlation effects tend to remove the possible appearance of charge bistability., Comment: 18 pages, 9 figures

We study the charge transfer dynamics following the formation of a phase or voltage biased su- perconducting nano-junction using a full counting statistics analysis. We demonstrate that the evolution of the zeros of the generating function allows one to identify the population of different many body states much in the same way as the accumulation of Yang-Lee zeros of the partition function in equilibrium statistical mechanics is connected to phase transitions. We give an exact expression connecting the dynamical zeros to the charge transfer cumulants and discuss when an approximation based on "dominant" zeros is valid. We show that, for generic values of the parameters, the system gets trapped into a metastable state characterized by a non-equilibrium population of the many body states which is dependent on the initial conditions. We study in particular the effect of the switching rates in the dynamics showing that, in contrast to intuition, the deviation from thermal equilibrium increases for the slower rates. In the voltage biased case the steady state is reached independently of the initial conditions. Our method allows us to obtain accurate results for the steady state current and noise in quantitative agreement with steady state methods developed to describe the multiple Andreev reflections regime. Finally, we discuss the system dynamics after a sudden voltage drop showing the possibility of tuning the many body states population by an appropriate choice of the initial voltage, providing a feasible experimental way to access the quench dynamics and control the state of the system., Comment: 19 pages, 27 figures

We analyze the quantum quench dynamics in the formation of a phase-biased superconducting nanojunction. We find that in the absence of an external relaxation mechanism and for very general conditions the system gets trapped in a metastable state, corresponding to a non-equilibrium population of the Andreev bound states. The use of the time-dependent Full Counting Statistics (FCS) analysis allows us to extract information on the asymptotic population of even and odd manybody states, demonstrating that a universal behavior, dependent only on the Andreev states energy, is reached in the quantum point contact limit. These results shed light on recent experimental observations on quasiparticle trapping in superconducting atomic contacts., Comment: 10 pages, 7 figures. Accepted for publication in Phys. Rev. Lett

We analyze the time-dependent full-counting statistics of charges transmitted through a quantum dot in the coherent regime. The generating function for the time-dependent charge transfer statistics is evaluated numerically by discretizing the Keldysh time contour, which allows us to compute the higher order charge and current cumulants. We also develop an analytic expression for all order cumulants at any time given as a function of the zeros of the generating function, finding that the short time universality is due to the presence of a dominant single zero. The robustness of the universal features at short times is studied in both the sequential and coherent regimes., Comment: 8 pages, 6 figures, invited contribution to special volume "FQMT'15: Frontiers of Quantum and Mesoscopic Thermodynamics (Prague, Czech Republic, 27 July - 1 August 2015)"

We develop a theoretical approach to study the transient dynamics and the time-dependent statistics for the Anderson-Holstein model in the regime of strong electron-phonon coupling. For this purpose we adapt a recently introduced diagrammatic approach to the time domain. The generating function for the time-dependent charge transfer probabilities is evaluated numerically by discretizing the Keldysh contour. The method allows us to analyze the system evolution to the steady state after a sudden connection of the dot to the leads, starting from different initial conditions. Simple analytical results are obtained in the regime of very short times. We study in particular the apparent bistable behavior occurring for strong electron-phonon coupling, small bias voltages and a detuned dot level. The results obtained are in remarkable good agreement with numerically exact results obtained by Quantum Monte Carlo methods. We analyze the waiting time distribution and charge transfer probabilities, showing that only a single electron transfer is responsible for the rich structure found in the short times regime. A universal scaling (independent of the model parameters) is found for the relative amplitude of the higher order current cumulants in the short times regime, starting from an initially empty dot. We finally analyze the convergence to the steady state of the differential conductance and of the differential Fano factor at the inelastic threshold, which exhibits a peculiar oscillatory behavior., Comment: 12 pages, 9 figures

We calculate the nonequilibrium local density of states on a vibrational quantum dot coupled to two electrodes at T=0 using a numerically exact diagrammatic Monte Carlo method. Our focus is on the interplay between the electron-phonon interaction strength and the bias voltage. We find that the spectral density exhibits a significant voltage dependence if the voltage window includes one or more phonon sidebands. A comparison with well-established approximate approaches indicates that this effect could be attributed to the nonequilibrium distribution of the phonons. Moreover, we discuss the long transient dynamics caused by the electron-phonon coupling., Comment: 9 pages, 11 figures

A theoretical approach for the non-equilibrium transport properties of nanoscale systems coupled to metallic electrodes with strong electron-phonon interactions is presented. It consists in a resummation of the dominant Feynman diagrams from the perturbative expansion in the coupling to the leads. We show that this scheme eliminates the main pathologies found in previous simple analytical approaches for the polaronic regime. The results for the spectral and transport properties are compared with those from several other approaches for a wide range of parameters. The method can be formulated in a simple way to obtain the full counting statistics. Results for the shot and thermal noise are presented., Comment: 11 pages, 11 figures. Accepted for publication in Physical Review B

Tunneling spectroscopy of a Nb coupled carbon nanotube quantum dot reveals the formation of pairs of Andreev bound states (ABS) within the superconducting gap. A weak replica of the lower ABS is found, which is generated by quasi-particle tunnelling from the ABS to the Al tunnel probe. An inversion of the ABS-dispersion is observed at elevated temperatures, which signals the thermal occupation of the upper ABS. Our experimental findings are well supported by model calculations based on the superconducting Anderson model., Comment: 6 pages, 7 figures

In this work, a new theoretical approach to study the non-equilibrium transport properties of nanoscale systems coupled to metallic electrodes with strong electron-phonon interactions is presented. The proposed approach consists in a resummation of the dominant Feynman diagrams from the exact preturbative expansion. This scheme is compared with methods that can be found in the literature. It shows a good agreement with these methods in the range where they are known to provide good results, for a wide range of parameters. Also, it is compared with path-integral Monte Carlo calculations giving a relatively good agreement for polaronic and non polaronic regimes. Some preliminary results for the current noise obtained with our method are presented., Comment: 24 pages and 14 figures. Master thesis presented at Universidad Aut\'onoma de Madrid on 27 May 2013

We calculate the time dependent nonequilibrium current through a single level quantum dot strongly coupled to a vibrational mode. The nonequilibrium real time dynamics caused by an instantaneous coupling of the leads to the quantum dot is discussed using an approximate method. The approach, which is specially designed for the strong polaronic regime, is based on the so-called polaron tunneling approximation. Considering different initial dot occupations, we show that a common steady state is reached after times much larger than the typical electron tunneling times due to a polaron blocking effect in the dot charge. A direct comparison is made with numerically exact data, showing good agreement for the time scales accessible by the diagrammatic Monte Carlo simulation method.

We analyze the spectral density of a single level quantum dot coupled to superconducting leads focusing on the Andreev states appearing within the superconducting gap. We use two complementary approaches: the numerical renormalization group and the Hartree-Fock approximation. Our results show the existence of up to four bound states within the gap when the ground state is a spin doublet (\pi\ phase). Furthermore the results demonstrate the reliability of the mean field description within this phase. This is understood from a complete correspondence that can be established between the exact and the mean field quasiparticle excitation spectrum, Comment: 6 pages, 5 figures

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 \pi-junction behavior, the interplay of Andreev and resonant tunneling, and the important role of Andreev bound states which 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., Comment: 39 pages, 54 figures, corresponds to a review article as submitted to Advances in Physics

We present a combined theoretical approach to study the nonequilibrium transport properties of nanoscale systems coupled to metallic electrodes and exhibiting strong electron-phonon interactions. We use the Keldysh Green function formalism to generalize beyond linear theory in the applied voltage an equation of motion method and an interpolative self-energy approximation previously developed in equilibrium. We analyze the specific characteristics of inelastic transport appearing in the intensity versus voltage curves and in the conductance, providing qualitative criteria for the sign of the step-like features in the conductance. Excellent overall agreement between both approaches is found for a wide range of parameters., Comment: 24 pages, 6 figures

We analyze the non-local transport properties of a d-wave superconductor coupled to metallic electrodes at nanoscale distances. We show that the non-local conductance exhibits an algebraical decay with distance rather than the exponential behavior which is found in conventional superconductors. Crossed Andreev processes, associated with electronic entanglement, are favored for certain orientations of the symmetry axes of the superconductor with respect to the leads. These properties would allow its experimental detection using present technologies., Comment: 5 pages, 5 figures

We present a theoretical approach to determine the electronic properties of nanoscale systems exhibiting strong electron-electron and electron-phonon interactions and coupled to metallic electrodes. This approach is based on an interpolative ansatz for the electronic self-energy which becomes exact both in the limit of weak and strong coupling to the electrodes. The method provides a generalization of previous interpolative schemes which have been applied to the purely electronic case extensively. As a test case we consider the single level Anderson-Holstein model. The results obtained with the interpolative ansatz are in good agreement with existing data from Numerical Renormalization Group calculations. We also check our results by considering the case of the electrodes represented by a few discrete levels which can be diagonalized exactly. The approximation describes properly the transition from the Kondo regime where electron-electron interactions dominate to the polaronic case characterized by a strong electron-phonon interaction., Comment: 8 pages, 7 figures, accepted for publication in Physical Review B

We present a theoretical analysis of the proximity effect at a graphene-superconductor interface. We use a tight-binding model for the electronic states in this system which allows to describe the interface at the microscopic level. Two different interface models are proposed: one in which the superconductor induces a finite pairing in the graphene regions underneath, thus maintaining the honeycomb structure at the interface and one that assumes that the graphene layer is directly coupled to a bulk superconducting electrode. We show that properties like the Andreev reflection probability and its channel decomposition depend critically on the model used to describe the interface. We also study the proximity effect on the local density of states on the graphene. For finite layers we analyze the induced minigap and how it is reduced when the length of the layer increases. Results for the local density of states profiles for finite and semi-infinite layers are presented., Comment: 9 pages, 7 figures, submitted to Phys. Rev. B

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., Comment: 8 pages, 7 figures

We analyze the ground state properties of an array of quantum dots connected in series between superconducting electrodes. This system is represented by a finite Hubbard chain coupled at both ends to BCS superconductors. The ground state is obtained using the Lanczos algorithm within a low energy theory in which the bulk superconductors are replaced by effective local pairing potentials. We study the conditions for the inversion of the sign of the Josephson coupling ($\pi$-junction behavior) as a function of the model parameters. Results are presented in the form of phase diagrams which provide a direct overall view of the general trends as the size of the system is increased, exhibiting a strong even-odd effect. The analysis of the spin-spin correlation functions and local charges give further insight into the nature of the ground state and how it is transformed by the presence of superconductivity in the leads. Finally we study the scaling of the Josephson current with the system size and relate these results with previous calculations of Josephson transport through a Luttinger liquid., Comment: 9 pages, 8 figures

Superconductors connected to normal metallic electrodes at the nanoscale provide a potential source of non-locally entangled electron pairs. Such states would arise from Cooper pairs splitting into two electrons with opposite spins tunnelling into different leads. In an actual system the detection of these processes is hindered by the elastic transmission of individual electrons between the leads, yielding an opposite contribution to the non-local conductance. Here we show that electromagnetic excitations on the superconductor can play an important role in altering the balance between these two processes, leading to a dominance of one upon the other depending on the spatial symmetry of these excitations. These findings allow to understand some intriguing recent experimental results and open the possibility to control non-local transport through a superconductor by an appropriate design of the experimental geometry., Comment: 6 pages, 3 figures

We analyze the magnetic and transport properties of a double quantum dot coupled to superconducting leads. In addition to the possible phase transition to a $\pi$ state, already present in the single dot case, this system exhibits a richer magnetic behavior due to the competition between Kondo and inter-dot antiferromagnetic coupling. We obtain results for the Josephson current which may help to understand recent experiments on superconductor-metallofullerene dimer junctions. We show that in such a system the Josephson effect can be used to control its magnetic configuration., Comment: 5 pages, 4 figures

The effect of electron-phonon interactions in the conductance through metallic atomic wires is theoretically analyzed. The proposed model allows to consider an atomic size region electrically and mechanically coupled to bulk electrodes. We show that under rather general conditions the features due to electron-phonon coupling are described by universal functions of the system transmission coefficients. It is predicted that the reduction of the conductance due to electron-phonon coupling which is observed close to perfect transmission should evolve into an enhancement at low transmission. This crossover can be understood in a transparent way as arising from the competition between elastic and inelastic processes., Comment: 5 pages, 5 figures

The inverse proximity effect, i.e. the induction of a magnetic moment in the superconductor in superconductor-ferromagnet (S/F) junctions is studied theoretically. We present a microscopic approach which combines a model Hamiltonian with elements of the well established quasiclassical theory. With its help we study systems with arbitrary degree of disorder, interface transparency and thickness of the layers. In the diffusive limit we recover the result of previous works: the direction of the induced magnetization $M$ is opposite to the one of the F layer. However, we show that in the ballistic case the sign of $M$ may be positive or negative depending on the quality of the interface and thickness of the layers. {We show that, regardless of its sign, the penetration length of the magnetic moment into the superconductor is of the order of the superconductor coherence length, which demonstrates that the effect has a superconducting origin.}, Comment: 10 pages; 7 figures. To be published in Phys. Rev. B

We present an experimental determination of the conduction channel distribution in lead nanoscale contacts with total conductances ranging from 1 to 15 G0, where G0=2e2/h. It is found that even for contacts having a cross section much smaller than the mean free path the distribution tends to be remarkably close to the universal diffusive limit. With the help of theoretical calculations we show that this behavior can be associated with the specific band structure of lead which produces a significant contribution of partially open channels even in the absence of atomic disorder. Published in Europhysics Letters, http://www.edpsciences.org/articles/epl/abs/2005/11/epl8748/epl8748.html

We analyze the dynamical Coulomb blockade of multiple Andreev reflections (MAR) in a superconducting quantum point contact coupled to a macroscopic impedance. We find that at very low transmission the blockade scales as $n^2$ with $n = {Int}(2\Delta/eV)$, where $V$ is the bias voltage and $\Delta$ is the superconducting gap, as it would correspond to the occurrence of "shots" of charge $ne$. For higher transmission the blockade is reduced both due to Pauli principle and to elastic renormalization of the MAR probability, and for certain voltage regions it may even become an "antiblockade", i.e. the current is enhanced due to the coupling with the electromagnetic environment., Comment: 5 pages, 4 figures, submitted to Phys. Rev. Lett

Combining ab-initio and self-consistent parametrized tight-binding calculations we analyze the conductance properties of atomic chains of 5d elements like Au, Pt and Ir. It is shown that, in addition to the even-odd parity oscillations characteristic of Au, conduction channels associated with the almost full d bands in Pt and Ir give rise to longer periods which could be observed in sufficiently long chains. The results for short chains are in good agreement with recent experimental measurements., Comment: 5 pages, 5 figures, to be published in Phys. Rev. B

We present a combined experimental and theoretical analysis of the low bias conductance properties of carbon nanotubes coupled to superconducting leads. In the Kondo regime the conductance exhibits a zero bias peak which can be several times larger than the unitary limit in the normal case. This zero bias peak can be understood by analyzing the dynamics of the subgap Andreev states under an applied bias voltage. It is shown that the existence of a linear regime is linked to the presence of a finite relaxation rate within the system. The theory provides a good fitting of the experimental results., Comment: 6 revtex4 pages, 6 figures, to appear in SSC

The transport properties of a quantum dot coupled to superconducting leads are analyzed. It is shown that the quasiparticle current in the Kondo regime is determined by the non-equilibrium dynamics of subgap states (Andreev states) under an applied voltage. The current at low bias is suppressed exponentially for decreasing Kondo temperature in agreement with recent experiments. We also predict novel interference effects due to multiple Landau-Zener transitions between Andreev states., Comment: Revtex4, 4 pages, 4 figures

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 band-width limit. The system exhibits a rich behavior as a function of the relevant parameters. We discuss in detail the conditions for the observation of Pi-junction behavior and the effect of Coulomb interactions on the Andreev states.

We analyze the current in a superconducting point contact of arbitrary transmission in the presence of a microwave radiation. The interplay between the ac Josephson current and the microwave signal gives rise to Shapiro steps at voltages V = (m/n) \hbar \omega_r/2e, where n,m are integer numbers and \omega_r is the radiation frequency. The subharmonic steps (n different from 1) are a consequence of the ocurrence of multiple Andreev reflections (MAR) and provide an unambiguous signature of the peculiar ac Josephson effect at high transmission. Moreover, the dc current exhibits a rich subgap structure due to photon-assisted MARs., Comment: Revtex, 4 pages, 4 figures

We analyze the current-voltage characteristic of a quantum conduction channel coupled to an electromagnetic environment of arbitrary frequency-dependent impedance. In the weak blockade regime the correction to the ohmic behavior is directly related to the channel current fluctuations vanishing at perfect transmission in the same way as shot noise. This relation can be generalized to describe the environmental Coulomb blockade in a generic mesoscopic conductor coupled to an external impedance, as the response of the latter to the current fluctuations in the former., Comment: 12 pages, 2 figures, submitted to Phys. Rev. Lett

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 self-energy 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., Comment: Revtex, 14 pages, 4 figures

Atomic quantum point contacts accommodate a small number of conduction channels. Their number N and transmission coefficients {T_n} can be determined by analyzing the subgap structure due to multiple Andreev reflections in the current-voltage (IV) characteristics in the superconducting state. With the help of mechanically controllable break-junctions we have produced Al contacts consisting of a small number of atoms. In the smallest stable contacts, usually three channels contribute to the transport. We show here that the channel ensemble {T_n} of few atom contacts remains unchanged up to temperatures and magnetic fields approaching the critical temperature and the critical field, respectively, giving experimental evidence for the prediction that the conduction channels are the same in the normal and in the superconducting state., Comment: 8 pages, 5 .eps figures. To be published in Physica B 223

We present an interpolative method for describing coherent transport through an interacting quantum dot. The idea of the method is to construct an approximate electron self-energy which becomes exact both in the limits of weak and strong coupling to the leads. The validity of the approximation is first checked for the case of a single (spin-degenerate) dot level. A generalization to the multilevel case is then discussed. We present results both for the density of states and the temperature dependent linear conductance showing the transition from the Kondo to the Coulomb blockade regime., Comment: 8 pages, 3 figures, includes lamuphys.sty, submitted to the Proceedings of the XVI Sitges Conference on Statistical Mechanics

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., Comment: 4 pages, revtex, submitted to PRL

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., Comment: RevTex, 10 pages, 3 eps figures. Submitted to PRL

We discuss the general transport properties of superconducting quantum point contacts. We show how these properties can be obtained from a microscopic model using nonequilibrium Green function techniques. For the case of a one-channel contact we analyze the response under different biasing conditions: constant applied voltage, current bias and microwave-induced transport. Current fluctuations are also analyzed with particular emphasis on thermal and shot-noise. Finally, the case of superconducting transport through a resonant level is discussed. The calculated properties show a remarkable agreement with the available experimental data from atomic-size contacts measurements. We suggest the possibility of extending this comparison to several other predictions of the theory., Comment: 10 pages, revtex, 8 figures, submitted to a special issue of Superlattices and Microstructures

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., Comment: 11 pages, 4 ps-figures. Submitted to Phys. Rev. Lett

The electronic and transport properties of atomic-size contacts are analyzed theoretically using a self-consistent tight-binding model. Our results show that, for s-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 this resonant states in scanning tunneling spectroscopy using sharp tips is briefly analized., Comment: 4 pages, 3 postscript figures, to be published in Phys.Rev.B

We address the problem of non-linear transport through discrete electronic levels in a small quantum dot coupled to superconducting electrodes. In our approach the low temperature I-V characteristics can be calculated including all multiple quasi-particle and Andreev processes. The limit of very weak coupling to the leads and large charging energies is briefly analyzed comparing the calculated lineshapes of the I-V curves with recent experimental results. When the coupling to the leads increases and Coulomb blockade effects can be neglected, the combination of multiple Andreev processes and resonant transmission gives rise to a rich subgap structure which largely differs from the one found in the more studied S-N-S systems. We show how multiple processes can be included within a simple sequential tunneling picture qualitatively explaining the subgap structure. We suggest an experimental set-up where the predicted effects could be observed., Comment: 11 pages, 4 postscript figures, to be published in Phys. Rev. B (rapid communications)

This manuscript contains a Comment on "Supercurrent Noise in Quantum Point Contacts" by D. Averin and H.T. Iman, Phys. Rev. Lett. 76, 3814 (1996) [cond-mat/9511128]., Comment: Revtex, 1 page, no figures ; Submitted to Phys. Rev. Lett

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 non-equilibrium 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 non-stationary 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., Comment: Revtex, 31 pages, 6 Postscript figures (ps-files uuencoded); submitted to PRB

We present a theory for the frequency-dependent current fluctuations in superconducting quantum point-contacts (SQPC) within the dc transport regime. This theory is valid for any barrier transparency between the tunnel and ballistic limits, yielding an analytical expression for the fluctuations spectrum in the subgap region. It is shown that the level of noise in a quasi-ballistic SQPC may have a huge increase in comparison with the case of a normal contact carrying the same average current. The effect of this high level of noise on the actual observability of the current-phase relation for a ballistic point-contact is discussed in connection with recent experimental measurements., Comment: 11 pages, REVTEX, including 2 Postscript figures

The exact expression for the phase-dependent linear conductance of a weakly damped superconducting quantum point contact is obtained. The calculation is performed by summing up the complete perturbative series in the coupling between the electrodes. The failure of any finite order perturbative expansion in the limit of small voltage and small quasi-particle damping is analyzed in detail. In the low transmission regime this nonperturbative calculation yields a result which is at variance with standard tunnel theory. Our result predicts the correct sign of the quasi-particle pair interference term and exhibits an unusual phase-dependence at low temperatures in qualitative agreement with the available experimental data., Comment: 12 pages (revtex) + 1 postscript figure. Submitted to Phys. Rev. Lett

A microscopic model for describing a superconducting mesoscopic weak link is presented. We consider a model geometry consisting of a narrow channel coupled to wider superconducting electrodes which act as reservoirs fixing the asymptotic values of the complex order parameter. For this model, the Bogoliubov-de Gennes equations are discretized and solved self-consistently using a non-equilibrium Green functions formalism. The transport properties and the electronic excitation spectra of this system are studied for the different regimes that can be reached by varying parameters like coherence length, constriction length, normal transmission coefficient and temperature. We study in detail the transition from the point contact limit to the infinite channel length case, analyzing the maximum Josephson current that can be sustained by the weak link as a function of its transmission coefficient and length., Comment: 23 pages (RevTex) 11 figures available upon request (fj@uamc10.fmc.uam.es)

We present a microscopic theory for the d.c. Josephson effect in model mesoscopic constrictions. Our method is based on a non-equilibrium Green function formalism which allows for a self-consistent determination of the order parameter profile along the constriction. The various regimes defined by the different length scales (Fermi wavelength $\lambda_F$, coherence length $\xi_0$ and constriction length $L_C$) can be analyzed, including the case where all these lengths are comparable. For the case $\lambda_F \tilde{<} (L_C,\xi_0)$ phase oscillations with spatial period $\lambda_F/2$ can be observed. In the case of $L_C>\xi_0$ solutions with a phase-slip center inside the constriction can be found, in agreement with previous phenomenological theories., Comment: 4 pages (RevTex 3.0), 3 postscript figures available upon request, 312456-CG

Correlation effects in the transport properties of a single quantum level coupled to electron reservoirs are discussed theoretically using a non-equilibrium Green functions approach. Our method is based on the introduction of a second-order self-energy associated with the Coulomb interaction that consistently eliminates the pathologies found in 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 finally discuss the experimental conditions for the simultaneous observation of these effects in an ultrasmall quantum dot., Comment: 4 pages (two columns), 3 figures under request