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

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