Josephson transport in superconducting quantum dots

Abstract: A single-level quantum dot connected to superconducting leads is an ideal system for studying the interplay between electronic correlations and the superconducting order. The proximity effect allows the Cooper pairs to leak into the quantum dot, opening a gap in its spectral function. Andreev reflections on the opposite interfaces give rise to discrete subgap states and the Coulomb interaction gives rise to the Kondo effect. This complex behavior in otherwise well controllable setup attracted a lot of attention in the past two decades and lead to many experimental realizations based on single molecules, carbon nanotubes or semiconducting nanowires as the central functional elements.
We describe the system by the single-impurity Anderson model coupled to BCS superconducting leads and optionally a third metallic lead and solve it using the quantum Monte Carlo method. We show how to include superconductivity into CT-HYB quantum Monte Carlo solver and compare the results with the self-consistent 2nd order perturbation theory and the numerical renormalization group. We show the drawbacks of various methods and comment on the behavior of the Josephson current in the vicinity of a quantum phase transition.

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