# Condensed Matter Seminar: "Quantum dot attached to superconducting leads: Andreev bound states and 0-pi transition"

#### Tuesday, September 5, 2017 - 11:30am

Carbon nanotubes with pronounced electron repulsion and well separated energy levels attached to superconducting leads display an impurity quantum phase transition at low temperatures from a spin singlet to a spin doublet state (0-pi transition). The transition is accompanied by a change of the sign of the Josephson current through the nanotube and by a crossing of the Andreev bound (Yu-Shiba-Rousinov gap) states. The quantum critical behavior is strongly influenced by electron correlations on the dot and reflects interplay of superconductivity and Kondo physics.We discuss a microscopic description of experimentally realized nanoscopic Josephson junctions via a single impurity Anderson model in a superconducting environment. We review the present status of the many-body perturbation theory and its ability to describe reliably the 0-pi transition. We compare various approximate solution resulting from the diagrammatic expansion with numerically exact methods, numerical renormalization group and continuous-time quantum Monte Carlo. We analyze the crossing of the Andreev bound states by splitting the spin symmetry and lifting the degeneracy of the pi phase by applying an external magnetic field.