Statistical correlation for the composite Boson

It is well known that the particles in a beam of Boson obeying Bose-Einstein statistics tend to cluster (bunching effect), while the particles in a degenerate beam of Fermion obeying Fermi-Dirac statistics expel each other (anti-bunching effect). Here we investigate, for the first time, the statistical correlation effect for the composite Boson, which is formed from a spin singlet entangled electron pair. By using nonequilibrium Green's function technique, we obtain a positive cross correlation for this kind of the composite Boson when the external voltage is smaller than the gap energy, which demonstrates that a spin singlet entangled electron pair looks like a composite Boson. In the larger voltage limit, the cross correlation becomes negative due to the contribution of the quasiparticles. At large voltages, the oscillation between Fermionic and Bosonic behavior of cross correlation is also observed in the strong coupling regime as one changes the position of the resonant levels. Our result can be easily tested in a three-terminal normal-superconductor-superconductor (N-S-S) hybrid mesoscopic system

Andreev tunnelling in quantum dots: A slave-boson approach

We study a strongly interacting quantum dot connected to a normal and to a superconducting lead. By means of the slave-boson technique we investigate the low temperature regime and discuss electrical transport through the dot. We find that the zero bias anomaly in the current-voltage characteristics which is associated to the occurance of the Kondo resonance in the quantum dot, is enhanced in the presence of superconductivity, due to resonant Andreev scattering.Comment: 4 pages, 1 figur

Influence of Supercurrents on Low-Temperature Thermopower in Mesoscopic N/S Structures

The thermopower of mesoscopic normal metal/superconductor structures has been measured at low temperatures. Effect of supercurrent present in normal part of the structure was studied in two cases: when it was created by applied external magnetic field and when it was applied directly using extra superconducting electrodes. Temperature and magnetic field dependencies of thermopower are compared to the numerical simulations based on the quasiclassical theory of the superconducting proximity effect.Comment: 21 pages, 12 figures. To be published in the proceedings of the ULTI conference organized in Lammi, Finland (2006

Reflectionless tunneling in ballistic normal-metal--superconductor junctions

We investigate the phenomenon of reflectionless tunneling in ballistic normal-metal--superconductor (NS) structures, using a semiclassical formalism. It is shown that applied magnetic field and superconducting phase difference both impair the constructive interference leading to this effect, but in a qualitatively different way. This is manifested both in the conductance and in the shot noise properties of the system considered. Unlike diffusive systems, the features of the conductance are sharp, and enable fine spatial control of the current, as well as single channel manipulations. We discuss the possibility of conducting experiments in ballistic semiconductor-superconductor structures with smooth interfaces and some of the phenomena, specific to such structures, that could be measured. A general criterion for the barrier at NS interfaces, though large, to be effectively transparent to pair current is obtained.Comment: published versio

Dissipative Electron Transport through Andreev Interferometers

We consider the conductance of an Andreev interferometer, i.e., a hybrid structure where a dissipative current flows through a mesoscopic normal (N) sample in contact with two superconducting (S) "mirrors". Giant conductance oscillations are predicted if the superconducting phase difference $\phi$ is varied. Conductance maxima appear when $\phi$ is on odd multiple of $\pi$ due to a bunching at the Fermi energy of quasiparticle energy levels formed by Andreev reflections at the N-S boundaries. For a ballistic normal sample the oscillation amplitude is giant and proportional to the number of open transverse modes. We estimate using both analytical and numerical methods how scattering and mode mixing --- which tend to lift the level degeneracy at the Fermi energy --- effect the giant oscillations. These are shown to survive in a diffusive sample at temperatures much smaller than the Thouless temperature provided there are potential barriers between the sample and the normal electron reservoirs. Our results are in good agreement with previous work on conductance oscillations of diffusive samples, which we propose can be understood in terms of a Feynman path integral description of quasiparticle trajectories.Comment: 24 pages, revtex, 12 figures in eps forma

Thermoelectric effects in superconducting proximity structures

Attaching a superconductor in good contact with a normal metal makes rise to a proximity effect where the superconducting correlations leak into the normal metal. An additional contact close to the first one makes it possible to carry a supercurrent through the metal. Forcing this supercurrent flow along with an additional quasiparticle current from one or many normal-metal reservoirs makes rise to many interesting effects. The supercurrent can be used to tune the local energy distribution function of the electrons. This mechanism also leads to finite thermoelectric effects even in the presence of electron-hole symmetry. Here we review these effects and discuss to which extent the existing observations of thermoelectric effects in metallic samples can be explained through the use of the dirty-limit quasiclassical theory.Comment: 14 pages, 10 figures. 374th WE-Heraus seminar: Spin physics of superconducting heterostructures, Bad Honnef, 200

Phase coherent transport in hybrid superconducting structures: the case of d-wave superconductors

We examine the effect of d-wave symmetry on zero bias anomalies in normal-superconducting tunnel junctions and phase-periodic conductances in Andreev interferometers. In the presence of d-wave pairing, zero-bias anomalies are suppressed compared with the s-wave case. For Andreev interferometers with aligned islands, the phase-periodic conductance is insensistive to the nature of the pairing, whereas for non-aligned islands, the nature of the zero-phase extremum is reversed.Comment: 10 Pages, Revtex. 11 postscript figures available on reques

Electron transport through strongly interacting quantum dot coupled to normal metal and superconductor

We study the electron transport through the quantum dot coupled to the normal metal and BCS-like superconductor (N - QD - S) in the presence of the Kondo effect and Andreev scattering. The system is described by the single impurity Anderson model in the limit of strong on-dot interaction. We use recently proposed equation of motion technique for Keldysh nonequilibrium Green's function together with the modified slave boson approach to study the electron transport. We derive formula for the current which contains various tunneling processes and apply it to study the transport through the system. We find that the Andreev conductance is strongly suppressed and there is no zero-bias (Kondo) anomaly in the differential conductance. We discuss effects of the particle-hole asymmetry in the electrodes as well as the asymmetry in the couplings.Comment: Supercond. Sci. Technol. - accepted for publicatio

Resonant Andreev reflections in superconductor-carbon-nanotube devices

Resonant Andreev reflection through superconductor-carbon-nanotube devices was investigated theoretically with a focus on the superconducting proximity effect. Consistent with a recent experiment, we find that for high transparency devices on-resonance, the Andreev current is characterized by a large value and a resistance dip; low-transparency off-resonance devices give the opposite result. We also give evidence that the observed low-temperature transport anomaly may be a natural result of Andreev reflection process

Random-Matrix Theory of Quantum Transport

This is a comprehensive review of the random-matrix approach to the theory of phase-coherent conduction in mesocopic systems. The theory is applied to a variety of physical phenomena in quantum dots and disordered wires, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction.Comment: 85 pages including 52 figures, to be published in Rev.Mod.Phy