The Andreev states of a superconducting quantum dot: mean field vs exact numerical results

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 spectrumComment: 6 pages, 5 figure

Interpolative method for transport properties of quantum dots in the Kondo regime

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 Mechanic

Quasiparticle trapping, Andreev level population dynamics, and charge imbalance in superconducting weak links

We present a comprehensive theoretical framework for the Andreev bound state population dynamics in superconducting weak links. Contrary to previous works, our approach takes into account the generated nonequilibrium distribution of the continuum quasiparticle states in a self-consistent way. As application of our theory, we show that the coupling of the superconducting contact to environmental phase fluctuations induces a charge imbalance of the continuum quasiparticle population. This imbalance is due to the breaking of the left-right symmetry in the rates connecting continuum quasiparticles and the Andreev bound state system, and causes a quasiparticle current on top of the Josephson current in a ring geometry. We evaluate the phase dependence of the quasiparticle current for realistic choices of the model parameters. Our theory also allows one to analyze the quantum coherent evolution of the system from an arbitrary initial state.Comment: 12 pages, 6 figures, final version (minor changes) to appear in PR

Microscopic theory of Cooper pair beam splitters based on carbon nanotubes

We analyze microscopically a Cooper pair splitting device in which a central superconducting lead is connected to two weakly coupled normal leads through a carbon nanotube. We determine the splitting efficiency at resonance in terms of geometrical and material parameters, including the effect of spin-orbit scattering. While the efficiency in the linear regime is limited to 50% and decay exponentially as a function of the width of the superconducting region we show that it can rise up to $\sim 100$ in the non-linear regime for certain regions of the stability diagram.Comment: 5 pages, 5 figure

Nonlinear effects of phonon fluctuations on transport through nanoscale junctions

We analyze the effect of electron-phonon coupling on the full counting statistics of a molecular junction beyond the lowest order perturbation theory. Our approach allows to take into account analytically the feedback between the non-equilibrium phonon and electronic distributions in the quantum regime. We show that even for junctions with high transmission and relatively weak electron-phonon coupling this feedback gives rise to increasingly higher nonlinearities in the voltage dependence of the cumulants of the transmitted charges distribution.Comment: 4 pages, 3 figure