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Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the 0-π transition

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Abstract

Behavior of Andreev gap states in a quantum dot with Coulomb repulsion symmetrically attached to superconducting leads is studied via the perturbation expansion in the interaction strength. We find the exact asymptotic form of the spin-symmetric solution for the Andreev states continuously approaching the Fermi level. We thereby derive a critical interaction at which the Andreev states at zero temperature merge at the Fermi energy, being the upper bound for the 0-π transition. We show that the spin-symmetric solution becomes degenerate beyond this interaction, in the π phase, and the Andreev states do not split unless the degeneracy is lifted. We further demonstrate that the degeneracy of the spin-symmetric state extends also into the 0 phase in which the solutions with zero and non-zero frequencies of the Andreev states may coexist.

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Authors and Affiliations

  1. Institute of Physics, The Czech Academy of Sciences, Na Slovance 2, 18221, Praha 8, Czech Republic

    Václav Janiš & Vladislav Pokorný

  2. Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, 12116, Praha 2, Czech Republic

    Martin Žonda

Authors
  1. Václav Janiš
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  2. Vladislav Pokorný
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  3. Martin Žonda
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Correspondence to Václav Janiš.

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Janiš, V., Pokorný, V. & Žonda, M. Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the 0-π transition. Eur. Phys. J. B 89, 197 (2016). https://doi.org/10.1140/epjb/e2016-70299-7

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  • DOI: https://doi.org/10.1140/epjb/e2016-70299-7

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