Wigner-Poisson Statistics of Topological Transitions in a Josephson Junction

C. W. J. Beenakker, J. M. Edge, J. P. Dahlhaus, D. I. Pikulin, Shuo Mi, and M. Wimmer
Phys. Rev. Lett. 111, 037001 – Published 17 July 2013
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Abstract

The phase-dependent bound states (Andreev levels) of a Josephson junction can cross at the Fermi level if the superconducting ground state switches between even and odd fermion parity. The level crossing is topologically protected, in the absence of time-reversal and spin-rotation symmetry, irrespective of whether the superconductor itself is topologically trivial or not. We develop a statistical theory of these topological transitions in an N-mode quantum-dot Josephson junction by associating the Andreev level crossings with the real eigenvalues of a random non-Hermitian matrix. The number of topological transitions in a 2π phase interval scales as N, and their spacing distribution is a hybrid of the Wigner and Poisson distributions of random-matrix theory.

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  • Received 14 May 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.037001

© 2013 American Physical Society

Authors & Affiliations

C. W. J. Beenakker, J. M. Edge, J. P. Dahlhaus, D. I. Pikulin, Shuo Mi, and M. Wimmer

  • Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

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Issue

Vol. 111, Iss. 3 — 19 July 2013

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