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arXiv · 1401.0738

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

V. Janiš·V. Pokorný·M. Žonda
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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 $0-\pi$ transition. We show that the spin-symmetric solution becomes degenerate beyond this interaction, in the $\pi$ 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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V. Janiš, V. Pokorný, M. Žonda. 2014-01-03. Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the $0-\pi$ transition. https://doi.org/10.1140/epjb/e2016-70299-7

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