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

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