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arXiv · 1501.07488

Perturbation theory of a superconducting $0-\pi$ impurity quantum phase transition

M. Žonda·V. Pokorný·V. Janiš·T. Novotný
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Abstract

A single-level quantum dot with Coulomb repulsion attached to two superconducting leads is studied via the perturbation expansion in the interaction strength. We use the Nambu formalism and the standard many-body diagrammatic representation of the impurity Green functions to formulate the Matsubara self-consistent perturbation expansion. We show that at zero temperature second order of the expansion in its $\it{spin-symmetric}$ version yields a nearly perfect agreement with the numerically exact calculations for the position of the $0-\pi$ phase boundary at which the Andreev bound states reach the Fermi energy as well as for the values of single-particle quantities in the 0-phase. We present results for phase diagrams, level occupation, induced local superconducting gap, Josephson current, and energy of the Andreev bound states with the precision surpassing any (semi)analytical approaches employed thus far.

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M. Žonda, V. Pokorný, V. Janiš, T. Novotný. 2015-01-29. Perturbation theory of a superconducting $0-\pi$ impurity quantum phase transition. https://doi.org/10.1038/srep08821

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